# Determine whether the system is consistent by setting up the appropriate augmented matrix and...

## Question:

Determine whether the system is consistent by setting up the appropriate augmented matrix and using elementary row operations to find an echelon form of the matrix.

{eq}x_1 - x_2 + 3x_3 = -9 {/eq}

{eq}-5x_1 + 5x_2 - 15x_3 = -2 {/eq}

{eq}x_1 + 5x_2 + x_3 = -17{/eq}

## Consistent Linear System

When we have a system of equations that relate multiple variables, this system doesn't always have a solution. If this system has at least one solution, then this system of equation is referred to as consistent. If it has no solutions, then it is inconsistent.

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To find whether or not this system is consistent, we need to try to solve it. Let's construct an augmented matrix and perform row operations in the...