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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

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Chapter
Section
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.]

3 x y z = 0

x + y + z = 4

To determine

To calculate: The solution of the given system of equations 3xyz=0,x+y+z=4 by the use of Gauss Jordan row reduction.

Explanation

Given Information:

The provided system of equations is,

3xyz=0x+y+z=4

Formula Used:

Elementary row operations:

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

Type 2: Replace the row Ri by aRi±bRj, where a and b is a nonzero real 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 a pivot.

Step 3: Make all elements below and above the pivot element zero in that column zero 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 1 using operations of type 1.

Calculation:

Consider the provided system of equations,

3xyz=0x+y+z=4

The augmented matrix for the given system of equations is,

[31101114]

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

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

The pivot element in the first row is 3.

[31101114]

Perform the operation R23R2R1,

[31101114][311004412]

Next, simplify the second row.

The pivot element in the second row is 4

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