Solve for x.

$$\left|\begin{array}{rr}-2 & -11 \\ x & 6\end{array}\right|=32$$

The system do not have unique solution. Solve the system, if possible.

$$\left\{\begin{array}{rr}3 x-4 y-6 z= & 10 \\ 2 x-4 y-5 z= & -14 \\ x-z= & 0\end{array}\right.$$

If

$$A=\left[\begin{array}{ll}1 & 5 \\ 3 & 2\end{array}\right]$$

and

$$B=\left[\begin{array}{rr}2 & 3 \\ -1 & -2\end{array}\right]$$

, compute A B and B A, if possible.

Use Cramer’s Rule to solve the system, if possible. If it is not possible, state whether the system is inconsistent or has infinitely many solutions.

$$\left\{\begin{array}{l}x+y+2 z=8 \\ 2 x+y+z=7 \\ 2 x+2 y+z=10\end{array}\right.$$

The system do not have unique solution. Solve the system, if possible.

$$\left\{\begin{array}{l}x+5 y-2 z=5 \\ x+3 y-2 z=23 \\ x+4 y-2 z=14\end{array}\right.$$

Use Cramer’s Rule to solve the system, if possible. If it is not possible, state whether the system is inconsistent or has infinitely many solutions.

$$\left\{\begin{array}{l}2 x-y-2 z=2 \\ 3 x-y+z=-3 \\ x+y-z=7\end{array}\right.$$

Find E F and F E if

$$E=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$$

and

$$F=\left[\begin{array}{ll}e & f \\ g & h\end{array}\right]$$

.

Find A B and B A if

$$A=\left[\begin{array}{lll}a & b & c \\ d & e & f\end{array}\right]$$

and

$$B=\left[\begin{array}{ll}1 & 2 \\ 3 & 4 \\ 5 & 6\end{array}\right]$$

Use Cramer’s Rule to solve the system, if possible. If it is not possible, state whether the system is inconsistent or has infinitely many solutions.

$$\left\{\begin{array}{l}x+y+z=3 \\ 2 x+y+z=4 \\ 2 x+2 y+z=5\end{array}\right.$$

The system do not have unique solution. Solve the system, if possible.

$$\left\{\begin{array}{r}x-y+2 z=-1 \\ 2 x+2 y+3 z=-3 \\ x+3 y+z=-2\end{array}\right.$$

Perform the matrix operation $A^2=A \cdot A$, if possible, with

$$\begin{array}{lll}A=\left[\begin{array}{rrr}1 & 3 & -3 \\ 2 & 4 & 1 \\ -1 & 3 & 2\end{array}\right] & B=\left[\begin{array}{rrr}1 & 2 & 1 \\ 2 & -1 & 3\end{array}\right] \\ C=\left[\begin{array}{rr}2 & 3 \\ -1 & 2 \\ 3 & -2\end{array}\right] \quad & D=\left[\begin{array}{lll}-2 & 3 & 1 \\ -3 & 2 & 2\end{array}\right]\end{array}$$

If C is a $3 \times 4$ matrix and D is a $4 \times 3$ matrix, what are the dimensions of C D and D C ?

Determine whether the planes represented by these following equations represent the same plane, parallel planes, or neither:

$$3 x-y+2 z=9 \text { and } 9 x-3 y+6 z=27$$

Use Cramer’s Rule to solve the system, if possible. If it is not possible, state whether the system is inconsistent or has infinitely many solutions.

$$\left\{\begin{array}{l}x-2 y=3 \\ -2 x+4 y=-6\end{array}\right.$$