## Vector Form for the General Solution of a System of Linear Equations

## Problem 267

Solve the following system of linear equations by transforming its augmented matrix to reduced echelon form (Gauss-Jordan elimination).

Find the vector form for the general solution.

\begin{align*}

x_1-x_3-3x_5&=1\\

3x_1+x_2-x_3+x_4-9x_5&=3\\

x_1-x_3+x_4-2x_5&=1.

\end{align*}