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Linear Algebra With Applications
Found in: Page 18
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

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Short Answer

In Exercises 1 through 12, find all solutions of the equations

with paper and pencil using Gauss–Jordan elimination.

Show all your work.

|x1+2x3+4x4=-8x2-3x-x4=63x1+4x2-6x3+8x4=0 -x2+3x3+4x4=-12|

For the given system of equation we have free variable is x3andx1=-2x3,x2=4+3x3,x4=-2.

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Step by Step Solution

Step 1: Augmented matrix

First of all we will make the augmented matrix to the corresponding system of equations.

Solving system of equations using gauss Jordan’s elimination method.


Corresponding Augmented matrix


Step 2: Solving the Augmented matrix


Proceeding for solving the augmented matrix



Corresponding system of equations

x1+2x3=0x2-3x3=4 x4=-2=x1=2x3x2=4+3x3 x4=-2

Here, we have x3is free variable.

Step 3: Values of variables

Since for free variables we can let any value for that.

We have free variablex3.

Let the value of x3=1


Step 4: Final answer

For the given system of equation is free variable x3andx1=-2x3,x2=4+3x3,x4=-2.

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