Find the addition of matrix [ A ] and [ B ] .

Question

Want to see more full solutions like this?

Answer 1

Question

Chapter 18, Problem 17P

(a)

To determine

Find the addition of matrix [A]and [B].

(a)

Expert Solution

Answer to Problem 17P

The addition of matrix [A] and [B] is [540123−450−4].

Explanation of Solution

Given data:

[A]=[42170−71−53],

[B]=[12−153345−7] and

[C]=[1−24]

Calculation:

Add two matrixes [A] and [B],

[A]+[B]=[42170−71−53]+[12−153345−7] (1)

Reduce the equation (1) as follows,

[A]+[B]=[4+12+21−17+50+3−7+31+4−5+53−7]=[540123−450−4]

Therefore, the addition of matrix [A] and [B] is [540123−450−4].

Conclusion:

Thus, the addition of matrix [A] and [B] is [540123−450−4].

(b)

To determine

Find the subtraction of matrix [A] and [B].

(b)

Expert Solution

Answer to Problem 17P

The subtraction of matrix [A] and [B] is [3022−3−10−3−1010].

Explanation of Solution

Given data:

[A]=[42170−71−53],

[B]=[12−153345−7] and

Calculation:

Subtract two matrixes A and B

[A]−[B]=[42170−71−53]−[12−153345−7] (2)

Reduce the equation (2) as follows,

[A]−[B]=[4−12−21−(−1)7−50−3−7−31−4−5−53−(−7)]=[3022−3−10−3−1010]

Therefore, the subtraction of matrix [A] and [B] is [3022−3−10−3−1010].

Conclusion:

Thus, the subtraction of matrix A and B is [3022−3−10−3−1010].

(c)

To determine

Find the value of 3[A].

(c)

Expert Solution

Answer to Problem 17P

The value of 3[A] is [1263210−213−159].

Explanation of Solution

Given data:

A=[42170−71−53]

Calculation:

Three times of matrix [A] is,

3[A]=3[42170−71−53] . (3)

Reduce equation (3) as follows,

3[A]=3[42170−71−53]3[A]=[3×43×23×13×73×03×(−7)3×13×(−5)3×3]

3[A]=[1263210−213−159]

Therefore, the value of 3[A] is [1263210−213−159].

Conclusion:

Thus, the value of 3[A] is [1263210−213−159].

(d)

To determine

Find the multiplication of matrix [A] and [B].

(d)

Expert Solution

Answer to Problem 17P

The multiplication of matrix [A] and [B] is [1819−5−21−2142−122−37].

Explanation of Solution

Given data:

A=[42170−71−53]

B=[12−153345−7]

C=[1−24]

Calculation:

Multiply the matrix [A] and [B],

[A][B]=[42170−71−53][12−153345−7] (4)

Reduce equation (4) as follows,

[A][B]=[42170−71−53][12−153345−7]=[4(1)+2(5)+1(4)4(2)+2(3)+1(5)4(−1)+2(3)+1(−7)7(1)+0(5)+(−7)(4)7(2)+0(3)+(−7)(5)7(−1)+0(3)+(−7)(−7)1(1)+(−5)(5)+3(4)1(2)+(−5)(3)+3(5)1(−1)+(−5)(3)+3(−7)]=[1819−5−21−2142−122−37]

Therefore, the multiplication of matrix [A] and [B] is [1819−5−21−2142−122−37].

Conclusion:

Therefore, the multiplication of matrix [A] and [B] is [1819−5−21−2142−122−37].

(e)

To determine

Find the multiplication of matrix [A] and [C].

(e)

Expert Solution

Answer to Problem 17P

The multiplication of matrix [A] and [C] is [4−2123].

Explanation of Solution

Given data:

[A]=[42170−71−53]

[C]=[1−24]

Calculation:

Multiply the matrix [A] and [C],

[A][C]=[42170−71−53][1−24] (5)

Reduce equation (5) as follows,

[A][C]=[42170−71−53][1−24]=[4(1)+2(−2)+1(4)7(1)+0(−2)+(−7)(4)1(1)+(−5)(−2)+3(4)]=[4−2123]

Therefore, the multiplication of matrix [A] and [C] is [4−2123].

Conclusion:

Therefore, the multiplication of matrix [A] and [C] is [4−2123].

(f)

To determine

Find the square of matrix [A].

(f)

Expert Solution

Answer to Problem 17P

The square of matrix [A] is [1819−5−21−2142−122−37].

Explanation of Solution

Given data:

A=[42170−71−53]

Calculation:

Square of the matrix [A],

[A]2=[A][A][A][A]=[42170−71−53][42170−71−53] (6)

Reduce equation (6) as follows,

[A]2=[42170−71−53][42170−71−53]=[4(4)+2(7)+1(1)4(2)+2(0)+1(−5)4(1)+2(−7)+1(3)7(4)+0(7)+(−7)(1)7(2)+0(0)+(−7)(−5)7(1)+0(−7)+(−7)(3)1(4)+(−5)(7)+3(1)1(2)+(−5)(0)+3(−5)1(1)+(−5)(−7)+3(3)]=[313−72149−14−28−1345]

Therefore, the square of matrix [A] is [313−72149−14−28−1345].

Conclusion:

Therefore, the square of matrix [A] is [313−72149−14−28−1345].

(g)

To determine

Prove the operation [I][A]=[A][I]=A.

(g)

Expert Solution

Explanation of Solution

Given data:

A=[42170−71−53]

Calculation:

[I] is the unit identity matrix [100010001].

Therefore,

[I][A]=[100010001][42170−71−53] (7)

Reduce equation (7) as follows,

[I][A]=[100010001][42170−71−53]=[1(4)+0(7)+0(1)1(2)+0(0)+0(−5)1(1)+0(−7)+0(3)0(4)+1(7)+0(1)0(2)+1(0)+0(−5)0(1)+1(−7)+0(3)0(4)+0(7)+1(1)0(2)+0(0)+1(−5)0(1)+0(−7)+1(3)]=[42170−71−53] (8)

Now,

[A][I]=[42170−71−53][100010001] (9)

Reduce equation (9) as follows,

[A][I]=[42170−71−53][100010001]=[4(1)+2(0)+1(0)4(0)+2(1)+1(0)4(0)+2(0)+1(1)7(1)+0(0)+(−7)(0)7(0)+0(1)+(−7)(0)7(0)+0(0)+(−7)(1)1(1)+(−5)(0)+3(0)1(0)+(−5)(1)+3(0)1(0)+(−5)(0)+3(1)]

[A][I]=[42170−71−53] (10)

Comparing equation (9) and (10),

[I][A]=[A][I]=A

Hence proved

Conclusion:

Thus, the operation [I][A]=[A][I]=A is proved.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Students have asked these similar questions

help me with this Question for revision purpose and as well with references The office building was built in year 2017 and has not obtained any Green Mark certification before. The office building is occupied by a single tenant/entity. The building management team had done an analysis of the building’s energy performance by extracting the data from the various systems. The current performance and findings of the systems are listed in Appendix A. The client is considering to have the building undergo retrofitting to improve the building’s energy performance. The objective is to achieve Green Mark Gold Plus under the new Green Mark 2021 framework. For part (a) below, you are to use Pathway 1: EUI for this. (a) As part of the feasibility exercise, you are to interpret the current performance of the existing building based on the data available (Refer to Appendix A). You should then organise and present to the client how does the current building relate to the Energy Efficiency Section of…

What are the advantages and disadvanages of using a bar chart in construction scheduling?

1- Determine the area of the region enclosed by y = t sin(t), the x- axis, y-axis and x = Π 元-3

Answer 2

Question

Chapter 18, Problem 17P

(a)

To determine

Find the addition of matrix [A]and [B].

(a)

Expert Solution

Answer to Problem 17P

The addition of matrix [A] and [B] is [540123−450−4].

Explanation of Solution

Given data:

[A]=[42170−71−53],

[B]=[12−153345−7] and

[C]=[1−24]

Calculation:

Add two matrixes [A] and [B],

[A]+[B]=[42170−71−53]+[12−153345−7] (1)

Reduce the equation (1) as follows,

[A]+[B]=[4+12+21−17+50+3−7+31+4−5+53−7]=[540123−450−4]

Therefore, the addition of matrix [A] and [B] is [540123−450−4].

Conclusion:

Thus, the addition of matrix [A] and [B] is [540123−450−4].

(b)

To determine

Find the subtraction of matrix [A] and [B].

(b)

Expert Solution

Answer to Problem 17P

The subtraction of matrix [A] and [B] is [3022−3−10−3−1010].

Explanation of Solution

Given data:

[A]=[42170−71−53],

[B]=[12−153345−7] and

Calculation:

Subtract two matrixes A and B

[A]−[B]=[42170−71−53]−[12−153345−7] (2)

Reduce the equation (2) as follows,

[A]−[B]=[4−12−21−(−1)7−50−3−7−31−4−5−53−(−7)]=[3022−3−10−3−1010]

Therefore, the subtraction of matrix [A] and [B] is [3022−3−10−3−1010].

Conclusion:

Thus, the subtraction of matrix A and B is [3022−3−10−3−1010].

(c)

To determine

Find the value of 3[A].

(c)

Expert Solution

Answer to Problem 17P

The value of 3[A] is [1263210−213−159].

Explanation of Solution

Given data:

A=[42170−71−53]

Calculation:

Three times of matrix [A] is,

3[A]=3[42170−71−53] . (3)

Reduce equation (3) as follows,

3[A]=3[42170−71−53]3[A]=[3×43×23×13×73×03×(−7)3×13×(−5)3×3]

3[A]=[1263210−213−159]

Therefore, the value of 3[A] is [1263210−213−159].

Conclusion:

Thus, the value of 3[A] is [1263210−213−159].

(d)

To determine

Find the multiplication of matrix [A] and [B].

(d)

Expert Solution

Answer to Problem 17P

The multiplication of matrix [A] and [B] is [1819−5−21−2142−122−37].

Explanation of Solution

Given data:

A=[42170−71−53]

B=[12−153345−7]

C=[1−24]

Calculation:

Multiply the matrix [A] and [B],

[A][B]=[42170−71−53][12−153345−7] (4)

Reduce equation (4) as follows,

[A][B]=[42170−71−53][12−153345−7]=[4(1)+2(5)+1(4)4(2)+2(3)+1(5)4(−1)+2(3)+1(−7)7(1)+0(5)+(−7)(4)7(2)+0(3)+(−7)(5)7(−1)+0(3)+(−7)(−7)1(1)+(−5)(5)+3(4)1(2)+(−5)(3)+3(5)1(−1)+(−5)(3)+3(−7)]=[1819−5−21−2142−122−37]

Therefore, the multiplication of matrix [A] and [B] is [1819−5−21−2142−122−37].

Conclusion:

Therefore, the multiplication of matrix [A] and [B] is [1819−5−21−2142−122−37].

(e)

To determine

Find the multiplication of matrix [A] and [C].

(e)

Expert Solution

Answer to Problem 17P

The multiplication of matrix [A] and [C] is [4−2123].

Explanation of Solution

Given data:

[A]=[42170−71−53]

[C]=[1−24]

Calculation:

Multiply the matrix [A] and [C],

[A][C]=[42170−71−53][1−24] (5)

Reduce equation (5) as follows,

[A][C]=[42170−71−53][1−24]=[4(1)+2(−2)+1(4)7(1)+0(−2)+(−7)(4)1(1)+(−5)(−2)+3(4)]=[4−2123]

Therefore, the multiplication of matrix [A] and [C] is [4−2123].

Conclusion:

Therefore, the multiplication of matrix [A] and [C] is [4−2123].

(f)

To determine

Find the square of matrix [A].

(f)

Expert Solution

Answer to Problem 17P

The square of matrix [A] is [1819−5−21−2142−122−37].

Explanation of Solution

Given data:

A=[42170−71−53]

Calculation:

Square of the matrix [A],

[A]2=[A][A][A][A]=[42170−71−53][42170−71−53] (6)

Reduce equation (6) as follows,

[A]2=[42170−71−53][42170−71−53]=[4(4)+2(7)+1(1)4(2)+2(0)+1(−5)4(1)+2(−7)+1(3)7(4)+0(7)+(−7)(1)7(2)+0(0)+(−7)(−5)7(1)+0(−7)+(−7)(3)1(4)+(−5)(7)+3(1)1(2)+(−5)(0)+3(−5)1(1)+(−5)(−7)+3(3)]=[313−72149−14−28−1345]

Therefore, the square of matrix [A] is [313−72149−14−28−1345].

Conclusion:

Therefore, the square of matrix [A] is [313−72149−14−28−1345].

(g)

To determine

Prove the operation [I][A]=[A][I]=A.

(g)

Expert Solution

Explanation of Solution

Given data:

A=[42170−71−53]

Calculation:

[I] is the unit identity matrix [100010001].

Therefore,

[I][A]=[100010001][42170−71−53] (7)

Reduce equation (7) as follows,

[I][A]=[100010001][42170−71−53]=[1(4)+0(7)+0(1)1(2)+0(0)+0(−5)1(1)+0(−7)+0(3)0(4)+1(7)+0(1)0(2)+1(0)+0(−5)0(1)+1(−7)+0(3)0(4)+0(7)+1(1)0(2)+0(0)+1(−5)0(1)+0(−7)+1(3)]=[42170−71−53] (8)

Now,

[A][I]=[42170−71−53][100010001] (9)

Reduce equation (9) as follows,

[A][I]=[42170−71−53][100010001]=[4(1)+2(0)+1(0)4(0)+2(1)+1(0)4(0)+2(0)+1(1)7(1)+0(0)+(−7)(0)7(0)+0(1)+(−7)(0)7(0)+0(0)+(−7)(1)1(1)+(−5)(0)+3(0)1(0)+(−5)(1)+3(0)1(0)+(−5)(0)+3(1)]

[A][I]=[42170−71−53] (10)

Comparing equation (9) and (10),

[I][A]=[A][I]=A

Hence proved

Conclusion:

Thus, the operation [I][A]=[A][I]=A is proved.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 18, Problem 17P

(a)

To determine

Find the addition of matrix [A]and [B].

(a)

Expert Solution

Answer to Problem 17P

The addition of matrix [A] and [B] is [540123−450−4].

Explanation of Solution

Given data:

[A]=[42170−71−53],

[B]=[12−153345−7] and

[C]=[1−24]

Calculation:

Add two matrixes [A] and [B],

[A]+[B]=[42170−71−53]+[12−153345−7] (1)

Reduce the equation (1) as follows,

[A]+[B]=[4+12+21−17+50+3−7+31+4−5+53−7]=[540123−450−4]

Therefore, the addition of matrix [A] and [B] is [540123−450−4].

Conclusion:

Thus, the addition of matrix [A] and [B] is [540123−450−4].

(b)

To determine

Find the subtraction of matrix [A] and [B].

(b)

Expert Solution

Answer to Problem 17P

The subtraction of matrix [A] and [B] is [3022−3−10−3−1010].

Explanation of Solution

Given data:

[A]=[42170−71−53],

[B]=[12−153345−7] and

Calculation:

Subtract two matrixes A and B

[A]−[B]=[42170−71−53]−[12−153345−7] (2)

Reduce the equation (2) as follows,

[A]−[B]=[4−12−21−(−1)7−50−3−7−31−4−5−53−(−7)]=[3022−3−10−3−1010]

Therefore, the subtraction of matrix [A] and [B] is [3022−3−10−3−1010].

Conclusion:

Thus, the subtraction of matrix A and B is [3022−3−10−3−1010].

(c)

To determine

Find the value of 3[A].

(c)

Expert Solution

Answer to Problem 17P

The value of 3[A] is [1263210−213−159].

Explanation of Solution

Given data:

A=[42170−71−53]

Calculation:

Three times of matrix [A] is,

3[A]=3[42170−71−53] . (3)

Reduce equation (3) as follows,

3[A]=3[42170−71−53]3[A]=[3×43×23×13×73×03×(−7)3×13×(−5)3×3]

3[A]=[1263210−213−159]

Therefore, the value of 3[A] is [1263210−213−159].

Conclusion:

Thus, the value of 3[A] is [1263210−213−159].

(d)

To determine

Find the multiplication of matrix [A] and [B].

(d)

Expert Solution

Answer to Problem 17P

The multiplication of matrix [A] and [B] is [1819−5−21−2142−122−37].

Explanation of Solution

Given data:

A=[42170−71−53]

B=[12−153345−7]

C=[1−24]

Calculation:

Multiply the matrix [A] and [B],

[A][B]=[42170−71−53][12−153345−7] (4)

Reduce equation (4) as follows,

[A][B]=[42170−71−53][12−153345−7]=[4(1)+2(5)+1(4)4(2)+2(3)+1(5)4(−1)+2(3)+1(−7)7(1)+0(5)+(−7)(4)7(2)+0(3)+(−7)(5)7(−1)+0(3)+(−7)(−7)1(1)+(−5)(5)+3(4)1(2)+(−5)(3)+3(5)1(−1)+(−5)(3)+3(−7)]=[1819−5−21−2142−122−37]

Therefore, the multiplication of matrix [A] and [B] is [1819−5−21−2142−122−37].

Conclusion:

Therefore, the multiplication of matrix [A] and [B] is [1819−5−21−2142−122−37].

(e)

To determine

Find the multiplication of matrix [A] and [C].

(e)

Expert Solution

Answer to Problem 17P

The multiplication of matrix [A] and [C] is [4−2123].

Explanation of Solution

Given data:

[A]=[42170−71−53]

[C]=[1−24]

Calculation:

Multiply the matrix [A] and [C],

[A][C]=[42170−71−53][1−24] (5)

Reduce equation (5) as follows,

[A][C]=[42170−71−53][1−24]=[4(1)+2(−2)+1(4)7(1)+0(−2)+(−7)(4)1(1)+(−5)(−2)+3(4)]=[4−2123]

Therefore, the multiplication of matrix [A] and [C] is [4−2123].

Conclusion:

Therefore, the multiplication of matrix [A] and [C] is [4−2123].

(f)

To determine

Find the square of matrix [A].

(f)

Expert Solution

Answer to Problem 17P

The square of matrix [A] is [1819−5−21−2142−122−37].

Explanation of Solution

Given data:

A=[42170−71−53]

Calculation:

Square of the matrix [A],

[A]2=[A][A][A][A]=[42170−71−53][42170−71−53] (6)

Reduce equation (6) as follows,

[A]2=[42170−71−53][42170−71−53]=[4(4)+2(7)+1(1)4(2)+2(0)+1(−5)4(1)+2(−7)+1(3)7(4)+0(7)+(−7)(1)7(2)+0(0)+(−7)(−5)7(1)+0(−7)+(−7)(3)1(4)+(−5)(7)+3(1)1(2)+(−5)(0)+3(−5)1(1)+(−5)(−7)+3(3)]=[313−72149−14−28−1345]

Therefore, the square of matrix [A] is [313−72149−14−28−1345].

Conclusion:

Therefore, the square of matrix [A] is [313−72149−14−28−1345].

(g)

To determine

Prove the operation [I][A]=[A][I]=A.

(g)

Expert Solution

Explanation of Solution

Given data:

A=[42170−71−53]

Calculation:

[I] is the unit identity matrix [100010001].

Therefore,

[I][A]=[100010001][42170−71−53] (7)

Reduce equation (7) as follows,

[I][A]=[100010001][42170−71−53]=[1(4)+0(7)+0(1)1(2)+0(0)+0(−5)1(1)+0(−7)+0(3)0(4)+1(7)+0(1)0(2)+1(0)+0(−5)0(1)+1(−7)+0(3)0(4)+0(7)+1(1)0(2)+0(0)+1(−5)0(1)+0(−7)+1(3)]=[42170−71−53] (8)

Now,

[A][I]=[42170−71−53][100010001] (9)

Reduce equation (9) as follows,

[A][I]=[42170−71−53][100010001]=[4(1)+2(0)+1(0)4(0)+2(1)+1(0)4(0)+2(0)+1(1)7(1)+0(0)+(−7)(0)7(0)+0(1)+(−7)(0)7(0)+0(0)+(−7)(1)1(1)+(−5)(0)+3(0)1(0)+(−5)(1)+3(0)1(0)+(−5)(0)+3(1)]

[A][I]=[42170−71−53] (10)

Comparing equation (9) and (10),

[I][A]=[A][I]=A

Hence proved

Conclusion:

Thus, the operation [I][A]=[A][I]=A is proved.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 18, Problem 17P

(a)

To determine

Find the addition of matrix [A]and [B].

(a)

Expert Solution

Answer to Problem 17P

The addition of matrix [A] and [B] is [540123−450−4].

Explanation of Solution

Given data:

[A]=[42170−71−53],

[B]=[12−153345−7] and

[C]=[1−24]

Calculation:

Add two matrixes [A] and [B],

[A]+[B]=[42170−71−53]+[12−153345−7] (1)

Reduce the equation (1) as follows,

[A]+[B]=[4+12+21−17+50+3−7+31+4−5+53−7]=[540123−450−4]

Therefore, the addition of matrix [A] and [B] is [540123−450−4].

Conclusion:

Thus, the addition of matrix [A] and [B] is [540123−450−4].

(b)

To determine

Find the subtraction of matrix [A] and [B].

(b)

Expert Solution

Answer to Problem 17P

The subtraction of matrix [A] and [B] is [3022−3−10−3−1010].

Explanation of Solution

Given data:

[A]=[42170−71−53],

[B]=[12−153345−7] and

Calculation:

Subtract two matrixes A and B

[A]−[B]=[42170−71−53]−[12−153345−7] (2)

Reduce the equation (2) as follows,

[A]−[B]=[4−12−21−(−1)7−50−3−7−31−4−5−53−(−7)]=[3022−3−10−3−1010]

Therefore, the subtraction of matrix [A] and [B] is [3022−3−10−3−1010].

Conclusion:

Thus, the subtraction of matrix A and B is [3022−3−10−3−1010].

(c)

To determine

Find the value of 3[A].

(c)

Expert Solution

Answer to Problem 17P

The value of 3[A] is [1263210−213−159].

Explanation of Solution

Given data:

A=[42170−71−53]

Calculation:

Three times of matrix [A] is,

3[A]=3[42170−71−53] . (3)

Reduce equation (3) as follows,

3[A]=3[42170−71−53]3[A]=[3×43×23×13×73×03×(−7)3×13×(−5)3×3]

3[A]=[1263210−213−159]

Therefore, the value of 3[A] is [1263210−213−159].

Conclusion:

Thus, the value of 3[A] is [1263210−213−159].

(d)

To determine

Find the multiplication of matrix [A] and [B].

(d)

Expert Solution

Answer to Problem 17P

The multiplication of matrix [A] and [B] is [1819−5−21−2142−122−37].

Explanation of Solution

Given data:

A=[42170−71−53]

B=[12−153345−7]

C=[1−24]

Calculation:

Multiply the matrix [A] and [B],

[A][B]=[42170−71−53][12−153345−7] (4)

Reduce equation (4) as follows,

[A][B]=[42170−71−53][12−153345−7]=[4(1)+2(5)+1(4)4(2)+2(3)+1(5)4(−1)+2(3)+1(−7)7(1)+0(5)+(−7)(4)7(2)+0(3)+(−7)(5)7(−1)+0(3)+(−7)(−7)1(1)+(−5)(5)+3(4)1(2)+(−5)(3)+3(5)1(−1)+(−5)(3)+3(−7)]=[1819−5−21−2142−122−37]

Therefore, the multiplication of matrix [A] and [B] is [1819−5−21−2142−122−37].

Conclusion:

Therefore, the multiplication of matrix [A] and [B] is [1819−5−21−2142−122−37].

(e)

To determine

Find the multiplication of matrix [A] and [C].

(e)

Expert Solution

Answer to Problem 17P

The multiplication of matrix [A] and [C] is [4−2123].

Explanation of Solution

Given data:

[A]=[42170−71−53]

[C]=[1−24]

Calculation:

Multiply the matrix [A] and [C],

[A][C]=[42170−71−53][1−24] (5)

Reduce equation (5) as follows,

[A][C]=[42170−71−53][1−24]=[4(1)+2(−2)+1(4)7(1)+0(−2)+(−7)(4)1(1)+(−5)(−2)+3(4)]=[4−2123]

Therefore, the multiplication of matrix [A] and [C] is [4−2123].

Conclusion:

Therefore, the multiplication of matrix [A] and [C] is [4−2123].

(f)

To determine

Find the square of matrix [A].

(f)

Expert Solution

Answer to Problem 17P

The square of matrix [A] is [1819−5−21−2142−122−37].

Explanation of Solution

Given data:

A=[42170−71−53]

Calculation:

Square of the matrix [A],

[A]2=[A][A][A][A]=[42170−71−53][42170−71−53] (6)

Reduce equation (6) as follows,

[A]2=[42170−71−53][42170−71−53]=[4(4)+2(7)+1(1)4(2)+2(0)+1(−5)4(1)+2(−7)+1(3)7(4)+0(7)+(−7)(1)7(2)+0(0)+(−7)(−5)7(1)+0(−7)+(−7)(3)1(4)+(−5)(7)+3(1)1(2)+(−5)(0)+3(−5)1(1)+(−5)(−7)+3(3)]=[313−72149−14−28−1345]

Therefore, the square of matrix [A] is [313−72149−14−28−1345].

Conclusion:

Therefore, the square of matrix [A] is [313−72149−14−28−1345].

(g)

To determine

Prove the operation [I][A]=[A][I]=A.

(g)

Expert Solution

Explanation of Solution

Given data:

A=[42170−71−53]

Calculation:

[I] is the unit identity matrix [100010001].

Therefore,

[I][A]=[100010001][42170−71−53] (7)

Reduce equation (7) as follows,

[I][A]=[100010001][42170−71−53]=[1(4)+0(7)+0(1)1(2)+0(0)+0(−5)1(1)+0(−7)+0(3)0(4)+1(7)+0(1)0(2)+1(0)+0(−5)0(1)+1(−7)+0(3)0(4)+0(7)+1(1)0(2)+0(0)+1(−5)0(1)+0(−7)+1(3)]=[42170−71−53] (8)

Now,

[A][I]=[42170−71−53][100010001] (9)

Reduce equation (9) as follows,

[A][I]=[42170−71−53][100010001]=[4(1)+2(0)+1(0)4(0)+2(1)+1(0)4(0)+2(0)+1(1)7(1)+0(0)+(−7)(0)7(0)+0(1)+(−7)(0)7(0)+0(0)+(−7)(1)1(1)+(−5)(0)+3(0)1(0)+(−5)(1)+3(0)1(0)+(−5)(0)+3(1)]

[A][I]=[42170−71−53] (10)

Comparing equation (9) and (10),

[I][A]=[A][I]=A

Hence proved

Conclusion:

Thus, the operation [I][A]=[A][I]=A is proved.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 18, Problem 17P

(a)

To determine

Find the addition of matrix [A]and [B].

(a)

Expert Solution

Answer to Problem 17P

The addition of matrix [A] and [B] is [540123−450−4].

Explanation of Solution

Given data:

[A]=[42170−71−53],

[B]=[12−153345−7] and

[C]=[1−24]

Calculation:

Add two matrixes [A] and [B],

[A]+[B]=[42170−71−53]+[12−153345−7] (1)

Reduce the equation (1) as follows,

[A]+[B]=[4+12+21−17+50+3−7+31+4−5+53−7]=[540123−450−4]

Therefore, the addition of matrix [A] and [B] is [540123−450−4].

Conclusion:

Thus, the addition of matrix [A] and [B] is [540123−450−4].

(b)

To determine

Find the subtraction of matrix [A] and [B].

(b)

Expert Solution

Answer to Problem 17P

The subtraction of matrix [A] and [B] is [3022−3−10−3−1010].

Explanation of Solution

Given data:

[A]=[42170−71−53],

[B]=[12−153345−7] and

Calculation:

Subtract two matrixes A and B

[A]−[B]=[42170−71−53]−[12−153345−7] (2)

Reduce the equation (2) as follows,

[A]−[B]=[4−12−21−(−1)7−50−3−7−31−4−5−53−(−7)]=[3022−3−10−3−1010]

Therefore, the subtraction of matrix [A] and [B] is [3022−3−10−3−1010].

Conclusion:

Thus, the subtraction of matrix A and B is [3022−3−10−3−1010].

(c)

To determine

Find the value of 3[A].

(c)

Expert Solution

Answer to Problem 17P

The value of 3[A] is [1263210−213−159].

Explanation of Solution

Given data:

A=[42170−71−53]

Calculation:

Three times of matrix [A] is,

3[A]=3[42170−71−53] . (3)

Reduce equation (3) as follows,

3[A]=3[42170−71−53]3[A]=[3×43×23×13×73×03×(−7)3×13×(−5)3×3]

3[A]=[1263210−213−159]

Therefore, the value of 3[A] is [1263210−213−159].

Conclusion:

Thus, the value of 3[A] is [1263210−213−159].

(d)

To determine

Find the multiplication of matrix [A] and [B].

(d)

Expert Solution

Answer to Problem 17P

The multiplication of matrix [A] and [B] is [1819−5−21−2142−122−37].

Explanation of Solution

Given data:

A=[42170−71−53]

B=[12−153345−7]

C=[1−24]

Calculation:

Multiply the matrix [A] and [B],

[A][B]=[42170−71−53][12−153345−7] (4)

Reduce equation (4) as follows,

[A][B]=[42170−71−53][12−153345−7]=[4(1)+2(5)+1(4)4(2)+2(3)+1(5)4(−1)+2(3)+1(−7)7(1)+0(5)+(−7)(4)7(2)+0(3)+(−7)(5)7(−1)+0(3)+(−7)(−7)1(1)+(−5)(5)+3(4)1(2)+(−5)(3)+3(5)1(−1)+(−5)(3)+3(−7)]=[1819−5−21−2142−122−37]

Therefore, the multiplication of matrix [A] and [B] is [1819−5−21−2142−122−37].

Conclusion:

Therefore, the multiplication of matrix [A] and [B] is [1819−5−21−2142−122−37].

(e)

To determine

Find the multiplication of matrix [A] and [C].

(e)

Expert Solution

Answer to Problem 17P

The multiplication of matrix [A] and [C] is [4−2123].

Explanation of Solution

Given data:

[A]=[42170−71−53]

[C]=[1−24]

Calculation:

Multiply the matrix [A] and [C],

[A][C]=[42170−71−53][1−24] (5)

Reduce equation (5) as follows,

[A][C]=[42170−71−53][1−24]=[4(1)+2(−2)+1(4)7(1)+0(−2)+(−7)(4)1(1)+(−5)(−2)+3(4)]=[4−2123]

Therefore, the multiplication of matrix [A] and [C] is [4−2123].

Conclusion:

Therefore, the multiplication of matrix [A] and [C] is [4−2123].

(f)

To determine

Find the square of matrix [A].

(f)

Expert Solution

Answer to Problem 17P

The square of matrix [A] is [1819−5−21−2142−122−37].

Explanation of Solution

Given data:

A=[42170−71−53]

Calculation:

Square of the matrix [A],

[A]2=[A][A][A][A]=[42170−71−53][42170−71−53] (6)

Reduce equation (6) as follows,

[A]2=[42170−71−53][42170−71−53]=[4(4)+2(7)+1(1)4(2)+2(0)+1(−5)4(1)+2(−7)+1(3)7(4)+0(7)+(−7)(1)7(2)+0(0)+(−7)(−5)7(1)+0(−7)+(−7)(3)1(4)+(−5)(7)+3(1)1(2)+(−5)(0)+3(−5)1(1)+(−5)(−7)+3(3)]=[313−72149−14−28−1345]

Therefore, the square of matrix [A] is [313−72149−14−28−1345].

Conclusion:

Therefore, the square of matrix [A] is [313−72149−14−28−1345].

(g)

To determine

Prove the operation [I][A]=[A][I]=A.

(g)

Expert Solution

Explanation of Solution

Given data:

A=[42170−71−53]

Calculation:

[I] is the unit identity matrix [100010001].

Therefore,

[I][A]=[100010001][42170−71−53] (7)

Reduce equation (7) as follows,

[I][A]=[100010001][42170−71−53]=[1(4)+0(7)+0(1)1(2)+0(0)+0(−5)1(1)+0(−7)+0(3)0(4)+1(7)+0(1)0(2)+1(0)+0(−5)0(1)+1(−7)+0(3)0(4)+0(7)+1(1)0(2)+0(0)+1(−5)0(1)+0(−7)+1(3)]=[42170−71−53] (8)

Now,

[A][I]=[42170−71−53][100010001] (9)

Reduce equation (9) as follows,

[A][I]=[42170−71−53][100010001]=[4(1)+2(0)+1(0)4(0)+2(1)+1(0)4(0)+2(0)+1(1)7(1)+0(0)+(−7)(0)7(0)+0(1)+(−7)(0)7(0)+0(0)+(−7)(1)1(1)+(−5)(0)+3(0)1(0)+(−5)(1)+3(0)1(0)+(−5)(0)+3(1)]

[A][I]=[42170−71−53] (10)

Comparing equation (9) and (10),

[I][A]=[A][I]=A

Hence proved

Conclusion:

Thus, the operation [I][A]=[A][I]=A is proved.

Answer 6

Chapter 18, Problem 17P

(a)

To determine

Find the addition of matrix [A]and [B].

(a)

Expert Solution

Answer to Problem 17P

The addition of matrix [A] and [B] is [540123−450−4].

Explanation of Solution

Given data:

[A]=[42170−71−53],

[B]=[12−153345−7] and

[C]=[1−24]

Calculation:

Add two matrixes [A] and [B],

[A]+[B]=[42170−71−53]+[12−153345−7] (1)

Reduce the equation (1) as follows,

[A]+[B]=[4+12+21−17+50+3−7+31+4−5+53−7]=[540123−450−4]

Therefore, the addition of matrix [A] and [B] is [540123−450−4].

Conclusion:

Thus, the addition of matrix [A] and [B] is [540123−450−4].

Answer 7

Chapter 18, Problem 17P

(a)

To determine

Find the addition of matrix [A]and [B].

Answer 8

(a)

Expert Solution

Answer to Problem 17P

The addition of matrix [A] and [B] is [540123−450−4].

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given data:

[A]=[42170−71−53],

[B]=[12−153345−7] and

[C]=[1−24]

Calculation:

Add two matrixes [A] and [B],

[A]+[B]=[42170−71−53]+[12−153345−7] (1)

Reduce the equation (1) as follows,

[A]+[B]=[4+12+21−17+50+3−7+31+4−5+53−7]=[540123−450−4]

Therefore, the addition of matrix [A] and [B] is [540123−450−4].

Conclusion:

Thus, the addition of matrix [A] and [B] is [540123−450−4].

Answer 13

(b)

To determine

Find the subtraction of matrix [A] and [B].

(b)

Expert Solution

Answer to Problem 17P

The subtraction of matrix [A] and [B] is [3022−3−10−3−1010].

Explanation of Solution

Given data:

[A]=[42170−71−53],

[B]=[12−153345−7] and

Calculation:

Subtract two matrixes A and B

[A]−[B]=[42170−71−53]−[12−153345−7] (2)

Reduce the equation (2) as follows,

[A]−[B]=[4−12−21−(−1)7−50−3−7−31−4−5−53−(−7)]=[3022−3−10−3−1010]

Therefore, the subtraction of matrix [A] and [B] is [3022−3−10−3−1010].

Conclusion:

Thus, the subtraction of matrix A and B is [3022−3−10−3−1010].

Answer 14

(b)

To determine

Find the subtraction of matrix [A] and [B].

Answer 15

(b)

Expert Solution

Answer to Problem 17P

The subtraction of matrix [A] and [B] is [3022−3−10−3−1010].

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given data:

[A]=[42170−71−53],

[B]=[12−153345−7] and

Calculation:

Subtract two matrixes A and B

[A]−[B]=[42170−71−53]−[12−153345−7] (2)

Reduce the equation (2) as follows,

[A]−[B]=[4−12−21−(−1)7−50−3−7−31−4−5−53−(−7)]=[3022−3−10−3−1010]

Therefore, the subtraction of matrix [A] and [B] is [3022−3−10−3−1010].

Conclusion:

Thus, the subtraction of matrix A and B is [3022−3−10−3−1010].

Answer 20

(c)

To determine

Find the value of 3[A].

(c)

Expert Solution

Answer to Problem 17P

The value of 3[A] is [1263210−213−159].

Explanation of Solution

Given data:

A=[42170−71−53]

Calculation:

Three times of matrix [A] is,

3[A]=3[42170−71−53] . (3)

Reduce equation (3) as follows,

3[A]=3[42170−71−53]3[A]=[3×43×23×13×73×03×(−7)3×13×(−5)3×3]

3[A]=[1263210−213−159]

Therefore, the value of 3[A] is [1263210−213−159].

Conclusion:

Thus, the value of 3[A] is [1263210−213−159].

Answer 21

(c)

To determine

Find the value of 3[A].

Answer 22

(c)

Expert Solution

Answer to Problem 17P

The value of 3[A] is [1263210−213−159].

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given data:

A=[42170−71−53]

Calculation:

Three times of matrix [A] is,

3[A]=3[42170−71−53] . (3)

Reduce equation (3) as follows,

3[A]=3[42170−71−53]3[A]=[3×43×23×13×73×03×(−7)3×13×(−5)3×3]

3[A]=[1263210−213−159]

Therefore, the value of 3[A] is [1263210−213−159].

Conclusion:

Thus, the value of 3[A] is [1263210−213−159].

Answer 27

(d)

To determine

Find the multiplication of matrix [A] and [B].

(d)

Expert Solution

Answer to Problem 17P

The multiplication of matrix [A] and [B] is [1819−5−21−2142−122−37].

Explanation of Solution

Given data:

A=[42170−71−53]

B=[12−153345−7]

C=[1−24]

Calculation:

Multiply the matrix [A] and [B],

[A][B]=[42170−71−53][12−153345−7] (4)

Reduce equation (4) as follows,

[A][B]=[42170−71−53][12−153345−7]=[4(1)+2(5)+1(4)4(2)+2(3)+1(5)4(−1)+2(3)+1(−7)7(1)+0(5)+(−7)(4)7(2)+0(3)+(−7)(5)7(−1)+0(3)+(−7)(−7)1(1)+(−5)(5)+3(4)1(2)+(−5)(3)+3(5)1(−1)+(−5)(3)+3(−7)]=[1819−5−21−2142−122−37]

Therefore, the multiplication of matrix [A] and [B] is [1819−5−21−2142−122−37].

Conclusion:

Therefore, the multiplication of matrix [A] and [B] is [1819−5−21−2142−122−37].

Answer 28

(d)

To determine

Find the multiplication of matrix [A] and [B].

Answer 29

(d)

Expert Solution

Answer to Problem 17P

The multiplication of matrix [A] and [B] is [1819−5−21−2142−122−37].

Answer 30

(d)

Expert Solution

Answer 31

(d)

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

Given data:

A=[42170−71−53]

B=[12−153345−7]

C=[1−24]

Calculation:

Multiply the matrix [A] and [B],

[A][B]=[42170−71−53][12−153345−7] (4)

Reduce equation (4) as follows,

[A][B]=[42170−71−53][12−153345−7]=[4(1)+2(5)+1(4)4(2)+2(3)+1(5)4(−1)+2(3)+1(−7)7(1)+0(5)+(−7)(4)7(2)+0(3)+(−7)(5)7(−1)+0(3)+(−7)(−7)1(1)+(−5)(5)+3(4)1(2)+(−5)(3)+3(5)1(−1)+(−5)(3)+3(−7)]=[1819−5−21−2142−122−37]

Therefore, the multiplication of matrix [A] and [B] is [1819−5−21−2142−122−37].

Conclusion:

Therefore, the multiplication of matrix [A] and [B] is [1819−5−21−2142−122−37].

Answer 34

(e)

To determine

Find the multiplication of matrix [A] and [C].

(e)

Expert Solution

Answer to Problem 17P

The multiplication of matrix [A] and [C] is [4−2123].

Explanation of Solution

Given data:

[A]=[42170−71−53]

[C]=[1−24]

Calculation:

Multiply the matrix [A] and [C],

[A][C]=[42170−71−53][1−24] (5)

Reduce equation (5) as follows,

[A][C]=[42170−71−53][1−24]=[4(1)+2(−2)+1(4)7(1)+0(−2)+(−7)(4)1(1)+(−5)(−2)+3(4)]=[4−2123]

Therefore, the multiplication of matrix [A] and [C] is [4−2123].

Conclusion:

Therefore, the multiplication of matrix [A] and [C] is [4−2123].

Answer 35

(e)

To determine

Find the multiplication of matrix [A] and [C].

Answer 36

(e)

Expert Solution

Answer to Problem 17P

The multiplication of matrix [A] and [C] is [4−2123].

Answer 37

(e)

Expert Solution

Answer 38

(e)

Expert Solution

Answer 39

Expert Solution

Answer 40

Explanation of Solution

Given data:

[A]=[42170−71−53]

[C]=[1−24]

Calculation:

Multiply the matrix [A] and [C],

[A][C]=[42170−71−53][1−24] (5)

Reduce equation (5) as follows,

[A][C]=[42170−71−53][1−24]=[4(1)+2(−2)+1(4)7(1)+0(−2)+(−7)(4)1(1)+(−5)(−2)+3(4)]=[4−2123]

Therefore, the multiplication of matrix [A] and [C] is [4−2123].

Conclusion:

Therefore, the multiplication of matrix [A] and [C] is [4−2123].

Answer 41

(f)

To determine

Find the square of matrix [A].

(f)

Expert Solution

Answer to Problem 17P

The square of matrix [A] is [1819−5−21−2142−122−37].

Explanation of Solution

Given data:

A=[42170−71−53]

Calculation:

Square of the matrix [A],

[A]2=[A][A][A][A]=[42170−71−53][42170−71−53] (6)

Reduce equation (6) as follows,

[A]2=[42170−71−53][42170−71−53]=[4(4)+2(7)+1(1)4(2)+2(0)+1(−5)4(1)+2(−7)+1(3)7(4)+0(7)+(−7)(1)7(2)+0(0)+(−7)(−5)7(1)+0(−7)+(−7)(3)1(4)+(−5)(7)+3(1)1(2)+(−5)(0)+3(−5)1(1)+(−5)(−7)+3(3)]=[313−72149−14−28−1345]

Therefore, the square of matrix [A] is [313−72149−14−28−1345].

Conclusion:

Therefore, the square of matrix [A] is [313−72149−14−28−1345].

Answer 42

(f)

To determine

Find the square of matrix [A].

Answer 43

(f)

Expert Solution

Answer to Problem 17P

The square of matrix [A] is [1819−5−21−2142−122−37].

Answer 44

(f)

Expert Solution

Answer 45

(f)

Expert Solution

Answer 46

Expert Solution

Answer 47

Explanation of Solution

Given data:

A=[42170−71−53]

Calculation:

Square of the matrix [A],

[A]2=[A][A][A][A]=[42170−71−53][42170−71−53] (6)

Reduce equation (6) as follows,

[A]2=[42170−71−53][42170−71−53]=[4(4)+2(7)+1(1)4(2)+2(0)+1(−5)4(1)+2(−7)+1(3)7(4)+0(7)+(−7)(1)7(2)+0(0)+(−7)(−5)7(1)+0(−7)+(−7)(3)1(4)+(−5)(7)+3(1)1(2)+(−5)(0)+3(−5)1(1)+(−5)(−7)+3(3)]=[313−72149−14−28−1345]

Therefore, the square of matrix [A] is [313−72149−14−28−1345].

Conclusion:

Therefore, the square of matrix [A] is [313−72149−14−28−1345].

Answer 48

(g)

To determine

Prove the operation [I][A]=[A][I]=A.

(g)

Expert Solution

Explanation of Solution

Given data:

A=[42170−71−53]

Calculation:

[I] is the unit identity matrix [100010001].

Therefore,

[I][A]=[100010001][42170−71−53] (7)

Reduce equation (7) as follows,

[I][A]=[100010001][42170−71−53]=[1(4)+0(7)+0(1)1(2)+0(0)+0(−5)1(1)+0(−7)+0(3)0(4)+1(7)+0(1)0(2)+1(0)+0(−5)0(1)+1(−7)+0(3)0(4)+0(7)+1(1)0(2)+0(0)+1(−5)0(1)+0(−7)+1(3)]=[42170−71−53] (8)

Now,

[A][I]=[42170−71−53][100010001] (9)

Reduce equation (9) as follows,

[A][I]=[42170−71−53][100010001]=[4(1)+2(0)+1(0)4(0)+2(1)+1(0)4(0)+2(0)+1(1)7(1)+0(0)+(−7)(0)7(0)+0(1)+(−7)(0)7(0)+0(0)+(−7)(1)1(1)+(−5)(0)+3(0)1(0)+(−5)(1)+3(0)1(0)+(−5)(0)+3(1)]

[A][I]=[42170−71−53] (10)

Comparing equation (9) and (10),

[I][A]=[A][I]=A

Hence proved

Conclusion:

Thus, the operation [I][A]=[A][I]=A is proved.

Answer 49

(g)

To determine

Prove the operation [I][A]=[A][I]=A.

Answer 50

(g)

Expert Solution

Explanation of Solution

Given data:

A=[42170−71−53]

Calculation:

[I] is the unit identity matrix [100010001].

Therefore,

[I][A]=[100010001][42170−71−53] (7)

Reduce equation (7) as follows,

[I][A]=[100010001][42170−71−53]=[1(4)+0(7)+0(1)1(2)+0(0)+0(−5)1(1)+0(−7)+0(3)0(4)+1(7)+0(1)0(2)+1(0)+0(−5)0(1)+1(−7)+0(3)0(4)+0(7)+1(1)0(2)+0(0)+1(−5)0(1)+0(−7)+1(3)]=[42170−71−53] (8)

Now,

[A][I]=[42170−71−53][100010001] (9)

Reduce equation (9) as follows,

[A][I]=[42170−71−53][100010001]=[4(1)+2(0)+1(0)4(0)+2(1)+1(0)4(0)+2(0)+1(1)7(1)+0(0)+(−7)(0)7(0)+0(1)+(−7)(0)7(0)+0(0)+(−7)(1)1(1)+(−5)(0)+3(0)1(0)+(−5)(1)+3(0)1(0)+(−5)(0)+3(1)]

[A][I]=[42170−71−53] (10)

Comparing equation (9) and (10),

[I][A]=[A][I]=A

Hence proved

Conclusion:

Thus, the operation [I][A]=[A][I]=A is proved.

Answer 51

(g)

Expert Solution

Answer 52

(g)

Expert Solution

Answer 53

Expert Solution

Answer 54

Ch. 18.2 - Prob. 1BYG Ch. 18.2 - Prob. 2BYG Ch. 18.2 - Prob. 3BYG Ch. 18.2 - Prob. 4BYG Ch. 18.2 - Prob. BYGV Ch. 18.3 - Prob. 1BYG Ch. 18.3 - Prob. 2BYG Ch. 18.3 - Prob. 3BYG Ch. 18.3 - Prob. BYGV Ch. 18.4 - Prob. 1BYG

Find the addition of matrix [ A ] and [ B ] .

Concept explainers

Find the addition of matrix [A]and [B].

Answer to Problem 17P

Explanation of Solution

Find the subtraction of matrix [A] and [B].

Answer to Problem 17P

Explanation of Solution

Find the value of 3[A].

Answer to Problem 17P

Explanation of Solution

Find the multiplication of matrix [A] and [B].

Answer to Problem 17P

Explanation of Solution

Find the multiplication of matrix [A] and [C].

Answer to Problem 17P

Explanation of Solution

Find the square of matrix [A].

Answer to Problem 17P

Explanation of Solution

Prove the operation [I][A]=[A][I]=A.

Explanation of Solution

Want to see more full solutions like this?

Chapter 18 Solutions