## Quiz 1. Gauss-Jordan Elimination / Homogeneous System. Math 2568 Spring 2017.

## Problem 262

**(a)** Solve the following system by transforming the augmented matrix to reduced echelon form (Gauss-Jordan elimination). Indicate the elementary row operations you performed.

\begin{align*}

x_1+x_2-x_5&=1\\

x_2+2x_3+x_4+3x_5&=1\\

x_1-x_3+x_4+x_5&=0

\end{align*}

**(b)** Determine all possibilities for the solution set of a homogeneous system of $2$ equations in $2$ unknowns that has a solution $x_1=1, x_2=5$.