Question

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

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

Short answer

$\left\{\begin{array}{l}2x-2y=0\\ 2y-z=2\\ 3x-z=-2\end{array}\right.$

Step-by-step solution

Step 1. Given Information

A matrix is given as-

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

Step 2. Calculating equations

Each row of the matrix represents an equation in three variables as $x,y\&z$.

The matrix given is a $3\times 4$matrix.

Assume first column as coefficients of variable $x$, similarly second for $y$and third for $z$.

Therefore the required system of equations is-

$\left\{\begin{array}{l}2x-2y=0\\ 2y-z=2\\ 3x-z=-2\end{array}\right.$