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December 29, 2014

December 29, 2014

Posted by **Wenny12** on Wednesday, April 20, 2011 at 12:18am.

Use Gauss-Jordan to solve

3x – 2y + z = 6

3x + y – z = -4

-x + 2y – 2z = -8

- Alg 2 - Math -
**MathMate**, Sunday, April 24, 2011 at 6:20amStart by transcribing the equations to a 3x4 matrix

3 -2 1 6

3 1 -1 -4

-1 2 -2 -8

The first step is to reduce each column to zero (except the diagonal element and above) by linear combination of rows. I'll do the first one:

3 -2 1 6

0 3 -2 -10 (row 2 - row 1)

0 4 -5 -18 (3*row 3 + row 1)

Continue:

3 -2 1 6

0 3 -2 -10

0 0 7 14 (4*row 2 - 3*row 3)

The last row can be simplified:

3 -2 1 6

0 3 -2 -10

0 0 1 2

So z=2, substitute z=2 in row 2 to eliminate elements above the diagonal

3 -2 0 4 (row 1 - row 3)

0 3 0 -6 (row 2 + 2*row 3)

0 0 1 2

Simplify row 2:

3 -2 0 4

0 1 0 -2 (row 2/3)

0 0 1 2

Now eliminate column 2 from row 1

3 0 0 0 (row 1 + 2*row 2)

0 1 0 -2

0 0 1 2

So

x=0

y=-2

z=2

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