Engineering Fundamentals: An Introduction to Engineering
Engineering Fundamentals: An Introduction to Engineering
6th Edition
ISBN: 9780357112311
Author: Saeed Moaveni
Publisher: Cengage Learning US
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Chapter 18, Problem 17P

(a)

To determine

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

(a)

Expert Solution
Check Mark

Answer to Problem 17P

The addition of matrix [A]and[B] is [5401234504].

Explanation of Solution

Given data:

[A]=[421707153],

[B]=[121533457] and

[C]=[124]

Calculation:

Add two matrixes [A]and[B],

[A]+[B]=[421707153]+[121533457] (1)

Reduce the equation (1) as follows,

[A]+[B]=[4+12+2117+50+37+31+45+537]=[5401234504]

Therefore, the addition of matrix [A]and[B] is [5401234504].

Conclusion:

Thus, the addition of matrix [A]and[B] is [5401234504].

(b)

To determine

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

(b)

Expert Solution
Check Mark

Answer to Problem 17P

The subtraction of matrix [A]and[B] is [302231031010].

Explanation of Solution

Given data:

[A]=[421707153],

[B]=[121533457] and

Calculation:

Subtract two matrixes AandB

[A][B]=[421707153][121533457] (2)

Reduce the equation (2) as follows,

[A][B]=[41221(1)75037314553(7)]=[302231031010]

Therefore, the subtraction of matrix [A]and[B] is [302231031010].

Conclusion:

Thus, the subtraction of matrix AandB is [302231031010].

(c)

To determine

Find the value of 3[A].

(c)

Expert Solution
Check Mark

Answer to Problem 17P

The value of 3[A] is [1263210213159].

Explanation of Solution

Given data:

A=[421707153]

Calculation:

Three times of matrix [A] is,

3[A]=3[421707153] . (3)

Reduce equation (3) as follows,

3[A]=3[421707153]3[A]=[3×43×23×13×73×03×(7)3×13×(5)3×3]

3[A]=[1263210213159]

Therefore, the value of  3[A] is [1263210213159].

Conclusion:

Thus, the value of  3[A] is [1263210213159].

(d)

To determine

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

(d)

Expert Solution
Check Mark

Answer to Problem 17P

The multiplication of matrix [A]and[B] is [1819521214212237].

Explanation of Solution

Given data:

A=[421707153]

B=[121533457]

C=[124]

Calculation:

Multiply the matrix [A]and[B],

[A][B]=[421707153][121533457] (4)

Reduce equation (4) as follows,

[A][B]=[421707153][121533457]=[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)]=[1819521214212237]

Therefore, the multiplication of matrix [A]and[B] is [1819521214212237].

Conclusion:

Therefore, the multiplication of matrix [A]and[B] is [1819521214212237].

(e)

To determine

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

(e)

Expert Solution
Check Mark

Answer to Problem 17P

The multiplication of matrix [A]and [C] is [42123].

Explanation of Solution

Given data:

[A]=[421707153]

[C]=[124]

Calculation:

Multiply the matrix [A]and [C],

[A][C]=[421707153][124] (5)

Reduce equation (5) as follows,

[A][C]=[421707153][124]=[4(1)+2(2)+1(4)7(1)+0(2)+(7)(4)1(1)+(5)(2)+3(4)]=[42123]

Therefore, the multiplication of matrix [A]and [C] is [42123].

Conclusion:

Therefore, the multiplication of matrix [A]and [C] is [42123].

(f)

To determine

Find the square of matrix [A].

(f)

Expert Solution
Check Mark

Answer to Problem 17P

The square of matrix [A] is [1819521214212237].

Explanation of Solution

Given data:

A=[421707153]

Calculation:

Square of the matrix [A],

[A]2=[A][A][A][A]=[421707153][421707153] (6)

Reduce equation (6) as follows,

[A]2=[421707153][421707153]=[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)]=[3137214914281345]

Therefore, the square of matrix [A] is [3137214914281345].

Conclusion:

Therefore, the square of matrix [A] is [3137214914281345].

(g)

To determine

Prove the operation  [I][A]=[A][I]=A.

(g)

Expert Solution
Check Mark

Explanation of Solution

Given data:

A=[421707153]

Calculation:

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

Therefore,

[I][A]=[100010001][421707153] (7)

Reduce equation (7) as follows,

[I][A]=[100010001][421707153]=[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)]=[421707153] (8)

Now,

[A][I]=[421707153][100010001] (9)

Reduce equation (9) as follows,

[A][I]=[421707153][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]=[421707153] (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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Engineering Fundamentals: An Introduction to Engineering

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