91Ó°ÊÓ

Find the value of each determinant. $$\left|\begin{array}{ll} 0 & 2 \\ 1 & 5 \end{array}\right|$$

Decide whether or not the given matrices are imerses of each other. (Hint: Check to see whether their products are the identity matrix \(I_{n-}\) ) $$\left[\begin{array}{rrr} 0 & 1 & 0 \\ 0 & 0 & -2 \\ 1 & -1 & 0 \end{array}\right] \text { and }\left[\begin{array}{rrr} 1 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & -1 & 0 \end{array}\right]$$

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

Find the value of each determinant. $$\left|\begin{array}{rr} 3 & 4 \\ 5 & -2 \end{array}\right|$$

Find the values of the variables for which each statement is true, if possible. $$\left[\begin{array}{rrc} 0 & 5 & x \\ -1 & 3 & y+2 \\ 4 & 1 & z \end{array}\right]=\left[\begin{array}{rrr} 0 & w & 6 \\ -1 & 3 & 0 \\ 4 & 1 & 8 \end{array}\right]$$

Solve each system by substitution. $$\begin{aligned} &4 x+3 y=-13\\\ &-x+y=5 \end{aligned}$$

Write the augmented matrix for each system and give its dimension. Do not solve. $$\begin{aligned}2 x+y+z-3 &=0 \\\3 x-4 y+2 z+7 &=0 \\\x+y+z-2 &=0\end{aligned}$$

Find the value of each determinant. $$\left|\begin{array}{rr} -9 & 7 \\ 2 & 6 \end{array}\right|$$

Find the partial fraction decomposition for each rational expression. \(=\) $$\frac{9}{x(x-3)}$$

Solve each system by substitution. $$\begin{array}{l} 3 x+4 y=4 \\ x-y=13 \end{array}$$