Solve the given systems of equations by using the inverse of the coefficient matrix. Use a calculator to perform the necessary matrix operations and display the results and the check. See Example 4.

4x + 2y – 2z = 2

3x –  2y8z = – 3

x + 3y + z = 10

Data from Example 4

Use a calculator to perform the necessary matrix operations in solving the following:

First, we set up matrices A, X, and C:

It is now necessary only to enter matrices A and C in the calculator and find the matrix product A⁻¹C, as shown in Fig. 16.13(a). (There is no need to record or display A−1.) This shows that the solution is

This solution can be checked on the calculator by storing the resulting matrix X as matrix B and finding the matrix product AB, which should equal matrix C as shown in Fig. 16.13(b). The product AB is equivalent to substituting each value into the original equations, as shown in Eq. (16.8).

Transcribed Image Text:

2r + 4st + - t + u = r - 2s + 3t s + 2t 3r + 4r + 5s 5 u = -4 - 4u = t + 3u = 8 - 1