Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
5th Edition
ISBN: 9780321816252
Author: C. Henry Edwards, David E. Penney, David Calvis
Publisher: PEARSON
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Textbook Question
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Chapter 5.1, Problem 1P

Let A = [ 2 3 4 7 ] and B = [ 3 4 5 1 ] .

Find (a) 2 A + 3 B ; (b) 3 A 2 B ; (c) A B ; (d) BA.

(a)

Expert Solution
Check Mark
Program Plan Intro

Program Description: Purpose ofproblem is to calculate the value of 2A+3B .

Summary introduction: Problem will use matrix additionin the matrices A=[2347]andB=[3451] .

Explanation of Solution

Given information:

The matrices A and B are,

  A=[2347]andB=[3451]

Explanation:

The given matrices A and B are,

  A=[2347]andB=[3451]

Multiply the matrix A by 2 and matrix B by 3 and then add them to obtain the value of 2A+3B is calculated as,

  2A+3B=2[ 2 3 4 7]+3[ 3 4 5 1]=[ 4 6 8 14]+[ 9 12 15 3]=[ 4+9 612 8+15 14+3]=[ 13 18 23 17]

The value of 2A+3B is [13182317] .

Conclusion:

Thus, thevalue of 2A+3B for the matrices A=[2347]andB=[3451] is [13182317] .

(b)

Expert Solution
Check Mark
Program Plan Intro

Program Description: Purpose ofproblem is to calculate the value of 3A2B .

Summary introduction: Problem will use matrix subtractionin the matrices A=[2347]andB=[3451] .

Explanation of Solution

Given information:

The matrices A and B are,

  A=[2347]andB=[3451]

Explanation:

The given matrices A and B are,

  A=[2347]andB=[3451]

Multiply the matrix A by 3 and matrix B by 2 and then subtract them to obtain the value of 3A2B is calculated as,

  3A2B=3[ 2 3 4 7]2[ 3 4 5 1]=[ 6 9 12 21][ 6 8 10 2]=[ 66 9+8 1210 212]=[ 0 1 2 19]

The value of 3A2B is [01219] .

Conclusion:

Thus, thevalue of 3A2B for the matrices A=[2347]andB=[3451] is [01219] .

(c)

Expert Solution
Check Mark
Program Plan Intro

Program Description: Purpose ofproblem is to calculate the value of AB .

Summary introduction: Problem will use matrix multiplicationin the matrices A=[2347]andB=[3451] .

Explanation of Solution

Given information:

The matrices A and B are,

  A=[2347]andB=[3451]

Explanation:

The matrices A and B are,

  A=[2347]andB=[3451]

The multiplication of matrix A and B is calculated as,

  AB=[ 2 3 4 7][ 3 4 5 1]=[ 615 83 12+35 16+7]=[ 9 11 47 9]

The value of AB is [911479] .

Conclusion:

Thus, thevalue of AB for the matrices A=[2347]andB=[3451] is [911479] .

(d)

Expert Solution
Check Mark
Program Plan Intro

Program Description: Purpose ofproblem is to calculate the value of BA .

Summary introduction: Problem will use matrix multiplication in the matrices A=[2347]andB=[3451] .

Explanation of Solution

Given information:

The matrices A and B are,

  A=[2347]andB=[3451]

Explanation:

The matrices A and B are,

  A=[2347]andB=[3451]

The multiplication of matrix B and A is calculated as,

  BA=[ 3 4 5 1][ 2 3 4 7]=[ 616 928 10+4 15+7]=[ 10 37 14 8]

The value of BA is [1037148] .

Conclusion:

Thus, thevalue of BA for the matrices A=[2347]andB=[3451] is [1037148] .

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Chapter 5 Solutions

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

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