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7th Edition

Stefan Waner + 1 other

Publisher: Cengage Learning

ISBN: 9781337280426

Chapter 3.2, Problem 32E

Textbook Problem

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In Exercises 1-42, use Gauss-Jordan row reduction to solve the given systems of equation. We suggest doing some by hand and others using technology. [*HINT:**See Examples 1-6.]*

To determine

**To calculate:** The solution of the given system of equations,

By the use of Gauss Jordan row reduction.

**Given Information:**

The system of equation is,

**Formula Used:**

Elementary row operations

Type 1: Replace the row

Type 2: Replace the row

Gauss Jordan reduction method:

Step 1: First clear the fractions or decimals if any, using operations of type 1.

Step 2: Select the first nonzero element of the first row as pivot.

Step 3: Use the pivot to clear its column using operations of type 2.

Step 4: Select the first nonzero element in the second row a pivot and clear its column.

Step 5: Select the first nonzero element in the third row a pivot and clear its column.

Step 6: Turn all the selected pivot elements into a 1 using operations of type 1.

**Calculation:**

Consider the system of equation,

The augmented matrix for the given system of equations is,

Apply Gauss Jordan reduction method to get the solution of the given system of equation.

Begin by, the simplification of the third row.

Perform the operation

Next pivot the first nonzero element of the first row and clear its column.

Perform the operation

Next clear the left over element of that column.

Perform the operation

Next simplify the second and fourth row.

Perform the operation

Next pivot the first nonzero element of the second row and clear its column

Finite Mathematics

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