91Ó°ÊÓ

Use Cramer's rule to solve each system or to determine that the system is inconsistent or contains dependent equations. $$ \begin{aligned}&2 x=3 y+2\\\&5 x=51-4 y\end{aligned} $$

In Exercises \(19-24\), perform each matrix row operation and write the new matrix. \(\left[\begin{array}{rrr|r}3 & -12 & 6 & 9 \\ 1 & -4 & 4 & 0 \\ 2 & 0 & 7 & 4\end{array}\right] \quad \frac{1}{3} R_{1}\)

In Exercises \(17-26,\) let $$ A=\left[\begin{array}{rr} -3 & -7 \\ 2 & -9 \\ 5 & 0 \end{array}\right] \text { and } B=\left[\begin{array}{rr} -5 & -1 \\ 0 & 0 \\ 3 & -4 \end{array}\right] $$ Solve each matrix equation for \(X\). $$ 3 X+2 A=B $$

find \(A^{-1}\) by forming \([A | I]\) and then using row operations to obtain [ \(I | B],\) where \(A^{-1}=[B]\) Check that \(A A^{-1}=I\) and \(A^{-1} A=I\) $$ A=\left[\begin{array}{rrr} 1 & -1 & 1 \\ 0 & 2 & -1 \\ 2 & 3 & 0 \end{array}\right] $$

In Exercises \(17-26,\) let $$ A=\left[\begin{array}{rr} -3 & -7 \\ 2 & -9 \\ 5 & 0 \end{array}\right] \text { and } B=\left[\begin{array}{rr} -5 & -1 \\ 0 & 0 \\ 3 & -4 \end{array}\right] $$ Solve each matrix equation for \(X\). $$ 2 X+5 A=B $$

Use Cramer's rule to solve each system or to determine that the system is inconsistent or contains dependent equations. $$ \begin{array}{rr}y= & -4 x+2 \\\2 x= & 3 y+8\end{array} $$

In Exercises \(19-24\), perform each matrix row operation and write the new matrix. \(\left[\begin{array}{rrr|r}1 & -3 & 2 & 0 \\ 3 & 1 & -1 & 7 \\ 2 & -2 & 1 & 3\end{array}\right] \quad-3 R_{1}+R_{2}\)

Use Gaussian elimination to find the complete solution to each system of equations, or show that none exists. $$\begin{aligned}w+2 x+3 y-z &=7 \\\2 x-3 y+z &=4 \\\w-4 x+y &=3\end{aligned}$$

In Exercises \(17-26,\) let $$ A=\left[\begin{array}{rr} -3 & -7 \\ 2 & -9 \\ 5 & 0 \end{array}\right] \text { and } B=\left[\begin{array}{rr} -5 & -1 \\ 0 & 0 \\ 3 & -4 \end{array}\right] $$ Solve each matrix equation for \(X\). $$ B-X=4 A $$

Use Cramer's rule to solve each system or to determine that the system is inconsistent or contains dependent equations. $$ \begin{aligned}&3 x=2-3 y\\\&2 y=3-2 x\end{aligned} $$