   # Solve the following system of simultaneous equations by the Gauss-Jordan method. −12 x 1 − 3 x 2 + 6 x 3 = 45 5 x 1 + 2 x 2 − 4 x 3 = −9 10 x 1 + x 2 − 7 x 3 = −32

#### Solutions

Chapter
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Chapter B, Problem 7P
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## Solve the following system of simultaneous equations by the Gauss-Jordan method.−12x1 − 3x2 + 6x3 = 455x1 + 2x2 − 4x3 = −910x1 + x2 − 7x3 = −32

To determine

Use the Gauss Jordan method to solve the simultaneous equations.

### Explanation of Solution

Given information:

12x13x2+6x3=455x1+2x24x3=910x1+x27x3=32

Calculation:

Write the system in the matrix form:

Ax=P[x1x12x3]=

Write the augmented matrix:

[12365241017|45932]

Divide the first row by 12.

[114125241017|154932]

In the second row, subtract the first row multiplied with 5 from second row.

[114125241017|154932]R2R25R1[1141255(1)25(14)45(12)1017|15495(154)32][11412034321017|15439432]

In the third row, subtract the first row multiplied with 10 from third row.

[11412034321017|15439432]R3R310R1[11412034321010×(1)110×(14)710×(12)|1543943210×(154)][11412034320322|154394112]

Divide the second row by 3/4.

[114120120322|15413112]

In the first row, subtract the second row multiplied with 14 from first row

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