91Ó°ÊÓ

Find the dimension of each matrix. Identify any square, column, or rove matrices. Do not use a calculator. $$\left[\begin{array}{ll}4 & 9\end{array}\right]$$

Determine whether A and B are imerses by calculating AB and BA. Do not use a calculator. $$A=\left[\begin{array}{lll} 1 & 2 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \end{array}\right] ; B=\left[\begin{array}{lll} 1 & -2 & 0 \\ 0 & 1 & 0 \\ 0 & -1 & 1 \end{array}\right]$$

Solve each system by substitution. $$\begin{aligned}5 x+y &=2 \\\y &=-3 x\end{aligned}$$

Solve each system by substitution. $$\begin{aligned}x+2 y &=-1 \\\2 x+y &=4\end{aligned}$$

Find the partial fraction decomposition for each rational expression. $$\frac{5}{3 x(2 x+1)}$$

Write the augmented matrix for each system. Do not solve the system. $$\begin{array}{r} 2 x+3 y=11 \\ x+2 y=8 \end{array}$$

Solve each system analytically. If the equations are dependent, write the solution set in terms of the variable \(z\). $$\begin{aligned} x+y+z &=5 \\ y+z &=2 \\ y-z &=0 \end{aligned}$$

Find each determinant. Do not use a calculator. $$\operatorname{det}\left[\begin{array}{rr}3 & 4 \\\5 & -2\end{array}\right]$$

Find the dimension of each matrix. Identify any square, column, or rove matrices. Do not use a calculator. $$[-9]$$

Determine whether A and B are imerses by calculating AB and BA. Do not use a calculator. $$A=\left[\begin{array}{rrr} -1 & -1 & -1 \\ 4 & 5 & 0 \\ 0 & 1 & -3 \end{array}\right] ; B=\left[\begin{array}{rrr} 15 & 4 & -5 \\ -12 & -3 & 4 \\ -4 & -1 & 1 \end{array}\right]$$