91Ó°ÊÓ

Evaluate each \(2 \times 2\) determinant. $$\left|\begin{array}{ll} 1 & 2 \\ 3 & 4 \end{array}\right|$$

solve each system of linear equations. $$\begin{array}{r} x-y+z=6 \\ -x+y+z=3 \\ -x-y-z=0 \end{array}$$

state the order of each matrix. $$\left[\begin{array}{rrr}-1 & 2 & 4 \\\7 & -3 & 9\end{array}\right]$$

Determine the order of each matrix. $$\left[\begin{array}{rrr} -1 & 3 & 4 \\ 2 & 7 & 9 \end{array}\right]$$

Solve each system of linear equations by substitution. $$\begin{aligned} &x+y=7\\\ &x-y=9 \end{aligned}$$

Match the rational expression \((1-6)\) with the form of the partial-fraction decomposition \((a-f)\). a. \(\frac{A}{x}+\frac{B}{x^{2}}+\frac{C x+D}{x^{2}+25}\) b. \(\frac{A}{x}+\frac{B x+C}{x^{2}+25}+\frac{D x+E}{\left(x^{2}+25\right)^{2}}\) c. \(\frac{A}{x}+\frac{B x+C}{x^{2}+25}\) d. \(\frac{A}{x}+\frac{B}{x+5}+\frac{C}{x-5}\) e. \(\frac{A}{x}+\frac{B}{x^{2}}+\frac{C x+D}{x^{2}+25}+\frac{E x+F}{\left(x^{2}+25\right)^{2}}\) f. \(\frac{A}{x}+\frac{B}{x^{2}}+\frac{C}{x+5}+\frac{D}{x-5}\) $$\frac{3 x+2}{x\left(x^{2}-25\right)}$$

Solve each system of linear equations by substitution. $$\begin{aligned} &x-y=-10\\\ &x+y=4 \end{aligned}$$

Evaluate each \(2 \times 2\) determinant. $$\left|\begin{array}{rr}1 & -2 \\\\-3 & -4\end{array}\right|$$

state the order of each matrix. $$\left[\begin{array}{rr}3 & 5 \\\2 & 6 \\\\-1 & -4\end{array}\right]$$

Determine the order of each matrix. $$\left[\begin{array}{ll} 0 & 1 \\ 3 & 9 \\ 7 & 8 \end{array}\right]$$