7. Systems of Equations & Matrices

Find the values of the variables for which each statement is true, if possible.

Evaluate each determinant.

Fill in the blank(s) to correctly complete each sentence. For the following statement to be true, the value of x must be ____, and the value of y must be ____.

Find the products AB and BA to determine whether B is the multiplicative inverse of A.

Are the given matrices inverses of each other? (Hint: Check to see whether their products are the identity matrix I_n.)

Evaluate each determinant in Exercises 1–10.

$\(\begin{vmatrix}\)-5 & -1 \\-2 & -7\(\end{vmatrix}\)$

Use the determinant theorems to evaluate each determinant. See Example 4.