91Ó°ÊÓ

For the following exercises, solve each system by Gaussian elimination. $$ \begin{array}{l}{0.1 x-0.2 y+0.3 z=2} \\ {0.5 x-0.1 y+0.4 z=8} \\ {0.7 x-0.2 y+0.3 z=8}\end{array} $$

Use the matrices below to perform the indicated operation if possible. If not possible, explain why the operation cannot be performed. \(A=\left[\begin{array}{rr}-10 & 20 \\ 5 & 25\end{array}\right], B=\left[\begin{array}{rr}40 & 10 \\ -20 & 30\end{array}\right], C=\left[\begin{array}{rr}-1 & 0 \\ 0 & -1 \\ 1 & 0\end{array}\right]\) \(B^{2} A^{2}\)

For the following exercises, find the decomposition of the partial fraction for the irreducible non repeating quadratic factor. $$\frac{4 x^{2}+5 x+3}{x^{3}-1}$$

For the following exercises, use any method to solve the nonlinear system. $$x^{2}+y^{2}-6 y=7$$ $$\quad\quad x^{2}+y=1$$

For the following exercises, solve a system using the inverse of a \(3 \times 3\) matrix. $$\begin{aligned} 6 x-5 y-z &=31 \\\\-x+2 y+z &=-6 \\ 3 x+3 y+2 z &=13 \end{aligned}$$

For the following exercises, solve the system of linear equations using Cramer's Rule. $$ \begin{aligned} 4 x+5 y-z &=-7 \\ -2 x-9 y+2 z &=8 \\ 5 y+7 z &=21 \end{aligned} $$

Solve each system by any method. $$ \begin{array}{r} \frac{7}{3} x-\frac{1}{6} y=2 \\ -\frac{21}{6} x+\frac{3}{12} y=-3 \end{array} $$

Find the decomposition of the partial fraction for the irreducible non repeating quadratic factor. \(\frac{4 x^{2}+5 x+3}{x^{3}-1}\)

Find the decomposition of the partial fraction for the irreducible non repeating quadratic factor. \(\frac{-5 x^{2}+18 x-4}{x^{3}+8}\)

Solve each system by Gaussian elimination. $$ \begin{array}{l} 0.2 x+0.1 y-0.3 z=0.2 \\ 0.8 x+0.4 y-1.2 z=0.1 \\ 1.6 x+0.8 y-2.4 z=0.2 \end{array} $$