7. Systems of Equations & Matrices

Given , and $C = \(\left\)[ \(\begin{matrix}\) -5 & 4 & 1 \\ 0 & 3 & 6 \(\end{matrix}\) \(\right\)]$, find each product, if possible. See Examples 5–7. AB

In Exercises 23–30, use expansion by minors to evaluate each determinant. $\(\begin{vmatrix}\)3 & 0 & 0 \\2 & 1 & -5 \\2 & 5 & -1\(\end{vmatrix}\)$

Perform each operation, if possible.

In Exercises 23–30, use expansion by minors to evaluate each determinant. $\(\begin{vmatrix}\)0.5 & 7 & 5 \\0.5 & 3 & 9 \\0.5 & 1 & 3\(\end{vmatrix}\)$

Find the inverse, if it exists, for each matrix.

Evaluate each determinant in Exercises 1–10.$\(\begin{vmatrix}\[\frac{1}{2}\) & \(\frac{1}{2}\) \\\(\frac{1}{8}\) & - \(\frac{3}{4}\]\end{vmatrix}\)$

What expression in x represents ?

Use Cramer's Rule to solve each system.

$\{\begin{array}{c}7x+2y=0\\ 2x+y=-3\end{array}$

Evaluate each determinant in Exercises 49–52. $\(\begin{vmatrix}\)-2 & -3 & 3 & 5 \\1 & -4 & 0 & 0 \\1 & 2 & 2 & -3 \\2 & 0 & 1 & 1\(\end{vmatrix}\)$

Find each sum or difference, if possible.

Write each matrix equation as a system of linear equations without matrices.

$\(\begin{bmatrix}\)2 & 0 & -1 \\0 & 3 & 0 \\1 & 1 & 0\(\end{bmatrix}\[\begin{bmatrix}\)x \\(\y\) \\(\z\]\end{bmatrix}\)=\(\begin{bmatrix}\)6 \\9 \\5\(\end{bmatrix}\)$

Find each sum or difference, if possible.

Evaluate each determinant in Exercises 1–10.

$\(\begin{vmatrix}\)-7 & 14 \\2 & -4\(\end{vmatrix}\)$

What is the value of x if ?

Given , and $C = \(\left\)[ \(\begin{matrix}\) -5 & 4 & 1 \\ 0 & 3 & 6 \(\end{matrix}\) \(\right\)]$, find each product, if possible. See Examples 5–7. BC