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.
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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