Chapter 1.3, Problem 21E

For the linear system in Example 5 of Section 1.2, express the general solution that we obtained in that example as a linear combination of column vectors that contain only numerical entries. [Suggestion: Rewrite the general solution as a single column vector, then write that column vector as a sum of column vectors each of which contains at most one parameter, and then factor out the parameters.]

EXAMPLE 5 | Gauss–Jordan Elimination

Solve by Gauss–Jordan elimination.

$\begin{array}{l}{x}_1+3x_2-2x_3+2x_5=0\\ 2x_1+6x_2-5x_3-2x_4+4x_5-3x_6=-1\\ 5x_3+10x_4+15x_6=5\\ 2x_1+6x_2+8x_4+4x_5+18x_6=6\end{array}$