Chapter 4.2, Problem 7E

### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Chapter
Section

### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

# 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.] 2 x + 3 y = 2 − x − 3 y 2 = − 1 2

To determine

To calculate: The solution of the given system of equations consisting of 2x+3y=2 and x32y=12 by the use of Gauss Jordan row reduction.

Explanation

Given Information:

The given system of equation is:

2x+3y=2āxā32y=ā12

Formula used:

Elementary row operations:

Type 1: Replacing the row Ri by aRi, where a is a nonzero number.

Type 2: Replacing the row Ri by aRiĀ±bRj, where a is a nonzero number.

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

Calculation:

Consider the system of equation:

2x+3y=2āxā32y=ā12

The augmented matrix for the given system of equations is:

[232ā1ā32ā12]

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

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