EBK PRECALCULUS W/LIMITS

4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter 8.3, Problem 50E

To determine

To solve the following system of linear equations using inverse matrix

${0.2x−0.6y=2.4−x+1.4y=−8.8$

Expert Solution & Answer

Answer to Problem 50E

$x=6,y=−2$

Explanation of Solution

Given:

${0.2x−0.6y=2.4−x+1.4y=−8.8$

Concept used:

To find inverse of a square matrix A, following steps should be followed.

Augment given matrix with the identity matrix
Perform row operations to make the identity matrix to the left and the right matrix becomes inverse matrix.

In this way, inverse matrix of a matrix can be obtained.

Formula used:

$AX=B⇔X=A−1B$

Calculation:

Consider given system of equations,

${0.2x−0.6y=2.4−x+1.4y=−8.8$

Writing above system of linear equations in matrix form $(AX=B)$ ,

$[0.2−0.6−11.4][xy]=[2.4−8.8]$

Here,

$A=[0.2−0.6−11.4]X=[xy]B=[2.4−8.8]$

Now, find the inverse matrix of matrix A.

Step 1: Augmenting matrix A with the identity matrix

$[0.2−0.6−11.41001]$

Step 2: Performing row operations to make the identity matrix to the left.

$[0.2−0.6−11.41001]Performing R2=R2+5R1[0.2−0.60−1.61051]Performing R1=5R1[1−30−1.65051]Performing R2=−0.625R2[1−30150−3.125−0.625]$

$Performing R1=R1+3R2[1001−4.375−1.875−3.125−0.625]$

So, inverse matrix is,

$A−1=[−4.375−1.875−3.125−0.625]$

Now, applying the formula $AX=B⇔X=A−1B$ ,

$[0.2−0.6−11.4][xy]=[2.4−8.8]⇔[xy]=[−4.375−1.875−3.125−0.625][2.4−8.8]$

Finding the solutions,

$⇒[xy]=[−4.375−1.875−3.125−0.625][2.4−8.8]⇒[xy]=[−4.375×2.4−1.875×(−8.8)−3.125×2.4−0.625×(−8.8)]⇒[xy]=[−10.5+16.5−7.5+5.5]⇒[xy]=[6−2]$

Conclusion:

Therefore, the solution to given system of equations is $x=6,y=−2.$

Chapter 8.3, Problem 49E

Chapter 8.3, Problem 51E

Chapter 8 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

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To solve the following system of linear equations using inverse matrix { 0.2 x − 0.6 y = 2.4 − x + 1.4 y = − 8.8

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Answer to Problem 50E

Explanation of Solution

Chapter 8 Solutions