   # Solve the following system of simultaneous equations by the Gauss-Jordan method. 5 x 1 − 2 x 2 + 6 x 3 = 0 −2 x 1 + 4 x 2 + x 3 + 3 x 4 = 18 6 x 1 + x 2 + 6 x 3 + 8 x 4 = −29 3 x 2 + 8 x 3 + 7 x 4 = 11

#### Solutions

Chapter
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Chapter B, Problem 8P
Textbook Problem
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## Solve the following system of simultaneous equations by the Gauss-Jordan method.5x1 − 2x2 + 6x3 = 0−2x1 + 4x2 + x3 + 3x4 = 186x1 + x2 + 6x3 + 8x4 = −293x2 + 8x3 + 7x4 = 11

To determine

Use the Gauss Jordan method to solve the simultaneous equations.

### Explanation of Solution

Given information:

5x12x2+6x3=02x1+4x2+x3+3x4=186x1+x2+6x3+8x4=293x2+8x3+7x4=11

Calculation:

Write the system in the matrix form:

Ax=P[x1x2x3x4]=

Write the augmented matrix:

[5260241361680387|0182911]

Divide the first row by 5.

[125650241361680387|0182911]

In the second row, subtract the first row multiplied with ­2 from second row.

[125650241361680387|0182911]R2R2(2)R1[1256502(2×1)4(2×25)1(2×65)361680387|0182911][1256500165175361680387|0182911]

In the third row, subtract the first row multiplied with ­6 from third row.

[1256500165175361680387|0182911]R3R36R1[1256500165175366×116×(25)66×(65)86×(0)0387|0182911][1256500165175301756580387|0182911]

Divide the second row by 16/5.

[125650011716151601756580387|04582911]

In the first row, subtract the second row multiplied with 25 from first row.

[125650011716151601756580387|04582911]R1R1(25R2)[125(25×1)65(25×1716)0(25×1516)011716151601756580387|0(25×458)4582911][1013838011716151601756580387|944582911]

In the third row, subtract the second row multiplied with 175  from third row.

[1013838011716151601756580387|944582911]R3R3(175)R2[101383801171615160175(175×1)65(175×1716)8(175×1516)0387|9445829(175×458)11][1013838011716151600771677160387|94458385811]

In the fourth row, subtract the second row multiplied with 3 from fourth row.

[1013838011716151600771677160387|94458385811]R4R43R2[101383801171615160077167716033×183×171673×1516|944583858113×458][1013838011716151600771677160077166716|944583858478]

Divide the third row by 7716

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