7. Systems of Equations & Matrices

Solve each equation.

Evaluate each determinant in Exercises 49–52. $\begin{vmatrix}4 & 2 & 8 & -7 \\-2 & 0 & 4 & 1 \\5 & 0 & 0 & 5 \\4 & 0 & 0 & -1\end{vmatrix}$

Evaluate each determinant.

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

$\begin{vmatrix}-4 & 1 & 4\\2& 0 & 1\\ 0&2&4\end{vmatrix}$

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

Evaluate each determinant.

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

In Exercises 53–54, evaluate each determinant. $\begin{vmatrix}\begin{vmatrix} 3 & 1 \\ -2 & 3 \end{vmatrix} & \begin{vmatrix} 7 & 0 \\ 1 & 5 \end{vmatrix} \\\begin{vmatrix} 3 & 0 \\ 0 & 7 \end{vmatrix} & \begin{vmatrix} 9 & -6 \\ 3 & 5 \end{vmatrix}\end{vmatrix}$

Use Cramer's Rule to solve each system.

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

Use the determinant theorems to evaluate each determinant.

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

In Exercises 55–56, write the system of linear equations for which Cramer's Rule yields the given determinants.

In Exercises 57–60, solve each equation for x.

Use the determinant theorems to evaluate each determinant.

In Exercises 57–60, solve each equation for x.