Chapter 1 - Systems of Linear Equations - 1.2 Gaussian Elimination and Gauss-Jordan Elimination - 1.2 Exercises - Page 23: 42

$x_{1}=0$ $x_{2}=-t$ $x_{3}=t$

The system of equations corresponding to given matrix is: $x_{1}=0$____________Equation 1 $x_{2}+x_{3}=0$________Equation 2 From equation 2 we have: $x_{2}=-x_{3}$ Using the parameter $t=x_{3}$ the solution is: $x_{1}=0$ $x_{2}=-t$ $x_{3}=t$