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.

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4xy + 2z2t+u 8x + y 2x 6y2z+t - u = 10 2x + 5y + z3t+8u = -22 4x - 3y + 2z + 4t + 2u -4 = -15 + 4t - 2u = 26