91Ó°ÊÓ

Write the system of equations that corresponds to the augmented matrix. $$ \left[\begin{array}{ll|l} 2 & -4 & -2 \\ 3 & -3 & -1 \end{array}\right] $$

Write the system of equations that corresponds to the augmented matrix. $$ \left[\begin{array}{rrr|r} 1 & 0 & -3 & -1 \\ 1 & -2 & 0 & -2 \\ 0 & -1 & 2 & 3 \end{array}\right] $$

Write the system of equations that corresponds to the augmented matrix. $$ \left[\begin{array}{rrr|r} 2 & -2 & 0 & -1 \\ 0 & 2 & -1 & 2 \\ 3 & 0 & -1 & -2 \end{array}\right] $$

In the following exercises, perform the indicated operations on the augmented matrices. $$\left[\begin{array}{rrr|r} 6 & -5 & 2 & 3 \\ 2 & 1 & -4 & 5 \\ 3 & -3 & 1 & -1 \end{array}\right]$$ (a) Interchange rows 2 and 3 (b) Multiply row 2 by 5 (c) Multiply row 3 by -2 and add to row 1 .

Perform the needed row operation that will get the first entry in row 2 to be zero in the augmented matrix: $$ \left[\begin{array}{rr|r} 1 & 2 & 5 \\ -3 & -4 & -1 \end{array}\right] $$

Perform the needed row operations that will get the first entry in both row 2 and row 3 to be zero in the augmented matrix: $$ \left[\begin{array}{rrr|r} 1 & -2 & 3 & -4 \\ 3 & -1 & -2 & 5 \\ 2 & -3 & -4 & -1 \end{array}\right] $$

In the following exercises, solve each system of equations using a matrix. $$ \left\\{\begin{array}{l} 2 x+y=2 \\ x-y=-2 \end{array}\right. $$

In the following exercises, solve each system of equations using a matrix. $$ \left\\{\begin{array}{l} 3 x+y=2 \\ x-y=2 \end{array}\right. $$

In the following exercises, solve each system of equations using a matrix. $$ \left\\{\begin{array}{l} -2 x+3 y=3 \\ x+3 y=12 \end{array}\right. $$

In the following exercises, solve each system of equations using a matrix. $$ \left\\{\begin{array}{l} 2 x-3 y+z=19 \\ -3 x+y-2 z=-15 \\ x+y+z=0 \end{array}\right. $$