Answer: Use Gaussian elimination with backward substitution and two-digit rounding
Chapter 6, Problem 3(choose chapter or problem)
Use Gaussian elimination with backward substitution and two-digit rounding arithmetic to solve the following linear systems. Do not reorder the equations. (The exact solution to each system is \(x_{1}=1, x_{2}=-1, x_{3}=3\).)
\(\begin{array}{l}\text{a.}\\ \begin{aligned}4 x_{1}-x_{2}+x_{3} & =8, \\ 2 x_{1}+5 x_{2}+2 x_{3} & =3, \\ x_{1}+2 x_{2}+4 x_{3} & =11 .\end{aligned}\end{array}\)
\(\begin{array}{l}\text{b.}\\ \begin{aligned}4 x_{1}+x_{2}+2 x_{3} & =9, \\ 2 x_{1}+4 x_{2}-x_{3} & =-5, \\ x_{1}+x_{2}-3 x_{3} & =-9 .\end{aligned}\end{array}\)
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