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Solution: Use Gaussian elimination with backward substitution and two-digit rounding
Chapter 6, Problem 4(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 \(x_{1}=-1\), \(x_{2}=1\), \(x_{3}=3\).)
a. \(\begin{aligned}-x_1+4x_2+x_3&=8,\\ \frac{5}{3}x_1+\frac{2}{3}x_2+\frac{2}{3}x_3&=1,\\ 2x_1+x_2+4x_3&=11.\end{aligned}\)
b. \(\begin{aligned} 4 x_{1}+2 x_{2}-x_{3} & =-5, \\ \frac{1}{9} x_{1}+\frac{1}{9} x_{2}-\frac{1}{3} x_{3} & =-1, \\ x_{1}+4 x_{2}+2 x_{3} & =9 . \end{aligned}\)
Questions & Answers
(1 Reviews)
QUESTION:
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 \(x_{1}=-1\), \(x_{2}=1\), \(x_{3}=3\).)
a. \(\begin{aligned}-x_1+4x_2+x_3&=8,\\ \frac{5}{3}x_1+\frac{2}{3}x_2+\frac{2}{3}x_3&=1,\\ 2x_1+x_2+4x_3&=11.\end{aligned}\)
b. \(\begin{aligned} 4 x_{1}+2 x_{2}-x_{3} & =-5, \\ \frac{1}{9} x_{1}+\frac{1}{9} x_{2}-\frac{1}{3} x_{3} & =-1, \\ x_{1}+4 x_{2}+2 x_{3} & =9 . \end{aligned}\)
ANSWER:Step 1 of 10
Given:- The equations:
(a). \(- {x_1} + 4{x_2} + {x_3} = 8\), \(\dfrac{5}{3}{x_1} + \dfrac{2}{3}{x_2} + \dfrac{2}{3}{x_3} = 1\), and \(2{x_1} + {x_2} + 4{x_3} = 11\).
(b). \(4{x_1} + 2{x_2} - {x_3} = - 5\), \(\frac{1}{9}{x_1} + \frac{1}{9}{x_2} - \frac{1}{3}{x_3} = - 1\), and \({x_1} + 4{x_2} + 2{x_3} = 9\).
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