91Ó°ÊÓ

Determine whether the matrix is in row-echelon form. If it is, determine whether it is also in reduced rew-echelon form. $$ \left[\begin{array}{llll} 1 & 0 & 2 & 1 \\ 0 & 1 & 3 & 4 \\ 0 & 0 & 1 & 0 \end{array}\right] $$

Graph the system of linear equations. Solve the system and interpret your answer. $$\begin{aligned}&0.2 x-0.5 y=-27.8\\\&0.3 x-0.4 y=68.7\end{aligned}$$

Graph the system of linear equations. Solve the system and interpret your answer. $$\begin{aligned}&\frac{x}{4}+\frac{y}{6}=1\\\&x-y=3\end{aligned}$$

Determine whether the matrix is in row-echelon form. If it is, determine whether it is also in reduced rew-echelon form. $$ \left[\begin{array}{lllll} 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 2 & 0 \end{array}\right] $$

Graph the system of linear equations. Solve the system and interpret your answer. $$\begin{aligned}&\frac{2 x}{3}+\frac{y}{6}=\frac{2}{3}\\\&4 x+y=4\end{aligned}$$

Determine whether the matrix is in row-echelon form. If it is, determine whether it is also in reduced rew-echelon form. $$ \left[\begin{array}{llll} 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 \end{array}\right] $$

Use backsubstitution to solve the system. $$\begin{aligned}x_{1}-x_{2} &=2 \\\x_{2} &=3\end{aligned}$$

Solve the system using either Gaussian elimination with back-substitution or Gauss-Jordan elimination. $$ \begin{aligned} &x+3 y=11\\\ &3 x+y=9 \end{aligned} $$

Solve the system using either Gaussian elimination with back-substitution or Gauss-Jordan elimination. $$ \begin{array}{rr} 2 x+6 y= & 16 \\ -2 x-6 y= & -16 \end{array} $$

Use backsubstitution to solve the system. $$\begin{aligned}2 x_{1}-4 x_{2} &=6 \\\3 x_{2} &=9\end{aligned}$$