Use the Gaussian Elimination Algorithm to solve the following linearsystems, if

Chapter 6, Problem 6

(choose chapter or problem)

Use the Gaussian Elimination Algorithm to solve the following linear systems, if possible, and determine whether row interchanges are necessary:

\(\begin{array}{l}\text{a.}\\ \begin{aligned}x_{2}-2 x_{3} & =4, \\ x_{1}-x_{2}+x_{3} & =6 \\ x_{1}-x_{3} & =2 .\end{aligned}\end{array}\)

\(\begin{aligned}b.\ \ x_1-\frac{1}{2}x_2+x_3&=4,\\ 2x_1-x_2-x_3+x_4&=5,\\ x_1+x_2+\frac{1}{2}x_3&=2,\\ x_1-\frac{1}{2}x_2+x_3+x_4&=5.\end{aligned}\)

\(\begin{aligned}c.\ 2x_1-x_2+x_3-x_4&=6,\\ x_2-x_3+x_4&=5,\\ x_4&=5,\\ x_3-x_4&=3.\end{aligned}\)

\(\begin{aligned}d.\ \ \ \ \ \ \ \ \ \ \ x_1+x_2+x_4&=2,\\ 2x_1+x_2-x_3+x_4&=1,\\ -x_1+2x_2+3x_3-x_4&=4,\\ 3x_1-x_2-x_3+2x_4&=-3.\end{aligned}\)