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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

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BuyFindarrow_forward

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 = 5

3 x + 2 y = 5

To determine

To calculate: The solution of the given system of equations consisting of 2x+3y=5 and 3x+2y=5 by the use of Gauss Jordan row reduction.

Explanation

Given Information:

The system of equations is:

2x+3y=53x+2y=5

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 aRi±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=53x+2y=5

The augmented matrix for the given system of equations is:

[235325]

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

Begin by the selection of the first nonzero element of first row and clearing its column.

Perform the operation R22R23R1,

[235325][235055]

Simplify the second row by the operation R215R2,

[235055

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