7. Systems of Equations & Matrices

In Exercises 23–30, use expansion by minors to evaluate each determinant. $\begin{vmatrix}1 & 1 & 1 \\2 & 2 & 2 \\-3 & 4 & -5\end{vmatrix}$

Write each linear system as a matrix equation in the form AX = B, where A is the coefficient matrix and B is the constant matrix.

$\begin{cases}6x + 5y = 13 \\5x + 4y = 10\end{cases}$

For each pair of matrices A and B, find (a) AB and (b) BA.

For Exercises 11–22, use Cramer's Rule to solve each system. $\begin{cases}x + y = 7 \\x - y = 3\end{cases}$

Write each linear system as a matrix equation in the form AX = B, where A is the coefficient matrix and B is the constant matrix.

$\begin{cases}x + 3y + 4z = -3 \\x + 2y + 3z = -2 \\x + 4y + 3z = -6\end{cases}$

Evaluate the determinant of the matrix.

Write each equation in standard form and use Cramer's Rule to solve the system.

$y=-3x+4$

$-2x=7y-9$

Evaluate the determinant of the matrix.

Solve the system of equations using Cramer's Rule.

$4x+2y+3z=6$

$x+y+z=3$

$5x+y+2z=5$

Write each equation in standard form and use Cramer's Rule to solve the system.

$y-9x=-3$

$-3x=4y-1$

What is the value of ?

Evaluate each determinant in Exercises 1–10.

$\begin{vmatrix}5 & 7 \\2 & 3\end{vmatrix}$

What expression in x represents ?

Evaluate each determinant in Exercises 1–10.

$\begin{vmatrix}-4 & 1 \\5 & 6\end{vmatrix}$

Evaluate each determinant in Exercises 1–10.

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