7. Systems of Equations & Matrices

For Exercises 11–22, use Cramer's Rule to solve each system. $\begin{cases}12x + 3y = 15 \\2x - 3y = 13\end{cases}$

Evaluate each determinant.

For Exercises 11–22, use Cramer's Rule to solve each system. $\begin{cases}4x - 5y = 17 \\2x + 3y = 3\end{cases}$

For Exercises 11–22, use Cramer's Rule to solve each system. $\begin{cases}x + 2y = 3 \\3x - 4y = 4\end{cases}$

Find the cofactor of each element in the second row of each matrix.

Find the cofactor of each element in the second row of each matrix.

For Exercises 11–22, use Cramer's Rule to solve each system. $\begin{cases}3x - 4y = 4 \\2x + 2y = 12\end{cases}$

Evaluate each determinant.

For Exercises 11–22, use Cramer's Rule to solve each system. $\begin{cases}2x = 3y + 2 \\5x = 51 - 4y\end{cases}$

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

Evaluate each determinant.

Evaluate each determinant.

In Exercises 23–30, use expansion by minors to evaluate each determinant. $\begin{vmatrix}3 & 1 & 0 \\-3 & 4 & 0 \\-1 & 3 & -5\end{vmatrix}$

Evaluate each determinant.

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