Question

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

Short answer

The required system of linear equations is $\left\{\begin{array}{l}x-3z=-1\\ x-2y=-2\\ -y+2z=3\end{array}\right.$.

Step-by-step solution

Step 1. Given information.

Consider the given augmented matrix,

$\left[\begin{array}{cccr}1& 0& -3& -1\\ 1& -2& 0& -2\\ 0& -1& 2& 3\end{array}\right]$

We know in an augmented matrix, each row corresponds to an equation. The vertical line replaces the equal sign in the equation. As this matrix is a$3\times 4$.

Step 2. Write the matrix into the system of equations.

Write into the system of equation with two variables,

$\left\{\begin{array}{l}x-3z=-1\\ x-2y=-2\\ -y+2z=3\end{array}\right.$