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

Question

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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.

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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.

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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.

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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.

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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

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

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

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Find the square of matrix [A].

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

Explanation of Solution

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