Solve the following system of equations using the Gaussian algorithm with column pivoting: a + 2b + c + 3d = 1 2a + 5b + 3c + d = 0 a + 6b + 2c + 2d = 1 a + 4b + c + d = 0. I know I have to switch first line and 2. Since the "2" in the first column is the new pivotelement. I am struggling with what to do afterwards. I know the solution is supposed to be: a= -1,b=0,c=1/2,d=1/2 How do I get there?

Solve the following system of equations using the Gaussian algorithm with column pivoting: a + 2b + c + 3d = 1 2a + 5b + 3c + d = 0 a + 6b + 2c + 2d = 1 a + 4b + c + d = 0. I know I have to switch first line and 2. Since the "2" in the first column is the new pivotelement. I am struggling with what to do afterwards. I know the solution is supposed to be: a= -1,b=0,c=1/2,d=1/2 How do I get there?

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 3BEXP

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Question

Solve the following system of equations using the Gaussian algorithm with column pivoting:
a + 2b + c + 3d = 1
2a + 5b + 3c + d = 0
a + 6b + 2c + 2d = 1
a + 4b + c + d = 0.

I know I have to switch first line and 2. Since the "2" in the first column is the new pivotelement.
I am struggling with what to do afterwards.

I know the solution is supposed to be:
a= -1,b=0,c=1/2,d=1/2

How do I get there?

Expert Solution