Saturday

November 1, 2014

November 1, 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

**Answer this Question**

**Related Questions**

Math - Use the Gauss-Jordan method to solve the equation: 3x-5y-2z=-9 -4x+3y+z=...

Pre-Calculus - Solve for x,y,z, & w using the Gauss-Jordan Elimination Method 5x...

Algebra - Use the Gauss-Jordan method to invert 1 0 0 2 -1 0 0 0 1 A1= 1 1 1 A2...

Algebra - Use Gauss-Jordan to solve 3x + 2y = -4 4x – 2y = -10

Algebra - Use Gauss-Jordan to solve 3x + 2y = -4 4x – 2y = -10

Math - How do I use gauss-jordan to solve this? Can you explain the steps and ...

math - solve by the gauss-jordan method x+y+z=6 3x+2y-z=4 3x+2y+2z=11

math - how do you solve x+y=2000;6x+8y=14400 using gauss-jordan elimination ...

algebra - 2x +y+3z=-1,(a+3)x+2y+8z=2,3x+y(a+1)z=1 solve for a, by gauss-jordan ...

MATH - solve the system of linear equations using the Gauss- Jordan elimination ...