   Chapter 11.3, Problem 53E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# SKILLS Plus 5 3 − 5 4 . Solving a matrix equation Solve the matrix equation by multiplying each side by the appropriate inverse matrix. [ 3 − 2 − 4 3 ] [ x y z u v w ] = [ 1 0 − 1 2 1 3 ]

To determine

To find:

The solution of the matrix equation [xyzuvw]= by multiplying the appropriate inverse matrix.

Explanation

Approach:

Two matrices A and B can be multiplied if they satisfy the condition that the number of columns in A is the same as the number of rows in B.

Two matrices A and B are said to be equal if the matrices have the same dimensions and each element of A is equal to the corresponding element of B.

If a 2×2 matrix A=[abcd], then

If adbc=0, then the inverse does not exist.

Calculation:

Let, A=, B= and X=[xyzuvw].

Thus, AX=B

The solution of AX=B can be given by

X=A1B …(1)

find A1 as follows.

Here, A=

Thus,

This implies, A1 exists, and its values is calculated as follows.

A1=11=

Substitute  for A1 and  for B in equation (1) to obtain the value of X

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