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.

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).

Equation 16.8

Transcribed Image Text:

x - 5y + 2z t = -18 3x + y 3z + 2t = 17 4x - 2y + z- t = -1 -2x + 3y - z + 4t = 11