Posted by **Lynn** on Wednesday, April 23, 2008 at 8:18pm.

I cannot come up with the right answers for my matrix.

I need to write as a system of equation and solve the system.

1 2 3 x 1

1 1 1 y = 12

-1 1 2 z 2

The answers I come up with are

31

15

15

when I check these, they will not work, what I am doing wrong?

- Math -
**Damon**, Wednesday, April 23, 2008 at 9:30pm
1 2 3 1

1 1 1 12

-1 1 2 2

I want the first column to be 1 0 0 so subtract second from first and add third to first

1 2 3 1

0 1 2 -11

0 3 5 3

I want the second column to be 0 1 0 so

subtract twice the second from the first and subtract 3 times the second from the third

1 0 -1 23

0 1 2 -11

0 0 -1 36

I want the third column to be 0 0 1 so multiply the third row by -1 first

1 0 -1 23

0 1 2 -11

0 0 1 -36

now add the third to the first and subtract twice the third from the second

1 0 0 -13

0 1 0 61

0 0 1 -36

so I get x = -13 , y = 61, z = -36

- Math -
**Damon**, Wednesday, April 23, 2008 at 9:33pm
when I am adding and subtracting I mean rows by the way.

- Math -
**Damon**, Wednesday, April 23, 2008 at 9:38pm
The idea is that I can add anything times and row to any other row, just as I can add anything times any equation to any other equation. In fact that is exactly what I am doing.

I select what I want to multiply each by to get an identity matrix on the left, column by column, thereby separating the variables. I am really solving the equations by elimination, just in a particular fashion.

- Math -
**Damon**, Wednesday, April 23, 2008 at 9:41pm
Oh, to write as a system of equations, multiply the coefficient matrix by the variable column

1 2 3 x 1

1 1 1 y = 12

-1 1 2 z 2

means

1 x + 2 y + 3 z = 1

1 x + 1 y + 1 z = 12

-1 x + 1 y + 2 z = 2

- Math -
**Damon**, Wednesday, April 23, 2008 at 10:05pm
Oh, the particular fashion is often called Gauss-Jordan reduction

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