91Ó°ÊÓ

Find the value of each variable. Do not use a calculator. $$\left[\begin{array}{ccc}a+2 & 1 & 5 m \\ 8 k & 0 & 3\end{array}\right]+\left[\begin{array}{ccc}3 a & 2 z & 5 m \\ 2 k & 5 & 6\end{array}\right]=\left[\begin{array}{ccc}10 & -14 & 80 \\ 10 & 5 & 9\end{array}\right]$$

Find each determinant. $$\operatorname{det}\left[\begin{array}{rrr}8 & -2 & -4 \\\7 & 0 & 3 \\\5 & -1 & 2\end{array}\right]$$

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

For each matrix, find \(A^{-1}\) if it exists. Do not use a calculator. $$A=\left[\begin{array}{rr} 5 & 10 \\ -3 & -6 \end{array}\right]$$

Solve each system by substitution. $$\begin{aligned}&7 x-y=-10\\\&3 y-x=10\end{aligned}$$

Write the system of equations associated with each augmented matrix. $$\left[\begin{array}{rr|r} 2 & 1 & 1 \\ 3 & -2 & -9 \end{array}\right]$$

For each matrix, find \(A^{-1}\) if it exists. Do not use a calculator. $$A=\left[\begin{array}{ll} 0.6 & 0.2 \\ 0.5 & 0.1 \end{array}\right]$$

Find the partial fraction decomposition for each rational expression. $$\frac{4}{x(1-x)}$$

Solve each system analytically. If the equations are dependent, write the solution set in terms of the variable \(z\). $$\begin{array}{r} x+3 y+4 z=14 \\ 2 x-3 y+2 z=10 \\ 3 x-y+z=9 \end{array}$$

Your friend missed the lecture on adding matrices. In your own words, explain to her how to add two matrices.