Question

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

Short answer

The required system of linear equations is$\left\{\begin{array}{l}2x-y=4\\ x-3y=2\end{array}\right.$.

Step-by-step solution

Step 1. Given information.

Consider the given augmented matrix,

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

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$2\times 3$.

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

Write into the system of equation with two variables,

$\left\{\begin{array}{l}2x-y=4\\ x-3y=2\end{array}\right.$