91Ó°ÊÓ

Find the cofactor of each element in the second row for each matrix. $$\left[\begin{array}{rrr}1 & -1 & 2 \\\1 & 0 & 2 \\\0 & -3 & 1\end{array}\right]$$

For each matrix, find \(A^{-1}\) if it exists. Do not use a calculator. $$A=\left[\begin{array}{ll} -5 & 3 \\ -8 & 5 \end{array}\right]$$

Write the augmented matrix for each system. Do not solve the system. $$\begin{aligned} 2 x+7 y &=1 \\ 5 x &=-15 \end{aligned}$$

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

If the equations are dependent, write the solution set in terms of the variable \(z\). (Hint: In Exercises 33-36, let \(t=\frac{1}{x}, u=\frac{1}{y},\) and \(v=\frac{1}{z} .\) Solve for \(t, u,\) and \(v,\) and then find \(x, y,\) and \(z\).) \begin{array}{r} 4 x-3 y+z=9 \\ 3 x+2 y-2 z=4 \\ x-y+3 z=5 \end{array}

Graph each inequality. Do not use a calculator. $$2 x>3-4 y$$

Write the augmented matrix for each system. Do not solve the system. $$\begin{aligned} 2 x+y+z &=3 \\ 3 x-4 y+2 z &=-7 \\ x+y+z &=2 \end{aligned}$$

For each matrix, find \(A^{-1}\) if it exists. Do not use a calculator. $$A=\left[\begin{array}{rr} -1 & -2 \\ 3 & 4 \end{array}\right]$$

Find the value of each variable. Do not use a calculator. $$\left[\begin{array}{rrc} 0 & 5 & x \\ -1 & 3 & y+2 \\ 4 & 1 & z \end{array}\right]=\left[\begin{array}{rrr} 0 & w+3 & 6 \\ -1 & 3 & 0 \\ 4 & 1 & 8 \end{array}\right]$$

Graph each inequality. Do not use a calculator. $$y<3 x^{2}+2$