Question

Write the system of equations that corresponds to the augmented matrix.

$\left[\begin{array}{ccc}2& -4& -2\\ 3& -3& -1\end{array}\right]$

Short answer

For the given augmented matrix $\left[\begin{array}{ccc}2& -4& -2\\ 3& -3& -1\end{array}\right]$, the system of equations is$\left\{\begin{array}{l}2x-4y=-2\\ 3x-3y=-1\end{array}\right.$.

Step-by-step solution

Step 1. Given Information

Consider the augmented matrix $\left[\begin{array}{ccc}2& -4& -2\\ 3& -3& -1\end{array}\right]$.

We need to find the corresponding system of equations.

Step 2. Write the system of equations

We remember that each row corresponds to an equation and that each entry is a coefficient of a variable or the constant. The vertical line replaces the equal sign. Since this matrix is a $3\times 2$, we know it will translate into a system of two equations with two variables. Thus the corresponding system of equations is

$\left[\begin{array}{ccc}2& -4& -2\\ 3& -3& -1\end{array}\right]\to \left\{\begin{array}{l}2x-4y=-2\\ 3x-3y=-1\end{array}\right.$