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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.


For the given system of equation x5,x5.are free variables and


See the step by step solution

Step by Step Solution

Step 1: Write the augmented matrix

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


The corresponding augmented matrix is written as:


Step 2: Solving the Augmented matrix

The above augmented matrix obtained above is already in reduced form, then the

System of equation to the corresponding above matrix will be


Step 3: Finding free variables

According to system x1=3+7x2-x5x3=2+2x5x4=1-x5, the variables x3,x4,x1 depend on x2,x5. So, x2,x5.are free variables.

Step 4: Final answer

Thus, for the given system of equation x2,x5 are free variables and x3=2+2x5,x4 =1-x5x1 =3+7x2-x5.

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