Solve the following system of equations using the Gaussian algorithm with column pivoting and backward insertion: 2x2 - 4x3 + x4 = -8x1 + 2x2 + 3x3 - x4 = 3-3x1 + 2x3 + 2x4 = -32x1 + x2 - x4 = 2 Here, column pivoting means that in the respective elimination stepsu. a row swap may be carried out in the respective elimination steps, so that the elimination elementa(m)mm is the largest element of the elimination column in terms of amount.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 2CEXP
Question

Solve the following system of equations using the Gaussian algorithm with column pivoting and backward insertion:


2x2 - 4x3 + x4 = -8
x1 + 2x2 + 3x3 - x4 = 3
-3x1 + 2x3 + 2x4 = -3
2x1 + x2 - x4 = 2


Here, column pivoting means that in the respective elimination steps
u. a row swap may be carried out in the respective elimination steps, so that the elimination element
a
(m)
mm is the largest element of the elimination column in terms of amount.

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