# Finding the inverse of a matrix

• May 5th 2011, 04:24 AM
brumby_3
Finding the inverse of a matrix
So I'm trying to find the inverse of the matrix:

[2 4 2]
[2 5 2]
[0 2 -1]

I've gotten up to this bit:

[1 0 5 | -1/2 -2 0]
[0 1 -2| 1/2 1 0]
[0 0 -3| 1 2 -1]

I can't figure out how to get a 1 on the bottom right corner or the remaining two 0's. Help would be appreciated!
• May 5th 2011, 04:42 AM
TheEmptySet
multiply row three by

$-\frac{1}{3}$

Then use it to get the zero's above it.
• May 5th 2011, 04:51 AM
brumby_3
Quote:

Originally Posted by TheEmptySet
multiply row three by

$-\frac{1}{3}$

Then use it to get the zero's above it.

I still don't know where to go from here, still confused :( I've done row 3 divided by-1/3, but still can't figure it out
• May 5th 2011, 05:54 AM
TheEmptySet
Quote:

Originally Posted by brumby_3
I still don't know where to go from here, still confused :( I've done row 3 divided by-1/3, but still can't figure it out

[1 0 5 | -1/2 -2 0]
[0 1 -2| 1/2 1 0]
[0 0 -3| 1 2 -1]

$\begin{bmatrix} 1 & 0 & 5 & -\frac{1}{2} & -2 & 0 \\ 0 & 1 & -2 & \frac{1}{2} & 1 & 0 \\ 0 & 0 & -3 & 1 & 2 & -1 \end{bmatrix}$

Now if you use

$-\frac{1}{3}R_3 \to R_3$

$\begin{bmatrix} 1 & 0 & 5 & -\frac{1}{2} & -2 & 0 \\ 0 & 1 & -2 & \frac{1}{2} & 1 & 0 \\ 0 & 0 & 1 & -\frac{1}{3} & \frac{2}{3} & -\frac{1}{3} \end{bmatrix}$

Now use the 1 in the to eliminate the the -2 and 5 above it
• May 5th 2011, 07:25 AM
brumby_3
Quote:

Originally Posted by TheEmptySet
[1 0 5 | -1/2 -2 0]
[0 1 -2| 1/2 1 0]
[0 0 -3| 1 2 -1]

$\begin{bmatrix} 1 & 0 & 5 & -\frac{1}{2} & -2 & 0 \\ 0 & 1 & -2 & \frac{1}{2} & 1 & 0 \\ 0 & 0 & -3 & 1 & 2 & -1 \end{bmatrix}$

Now if you use

$-\frac{1}{3}R_3 \to R_3$

$\begin{bmatrix} 1 & 0 & 5 & -\frac{1}{2} & -2 & 0 \\ 0 & 1 & -2 & \frac{1}{2} & 1 & 0 \\ 0 & 0 & 1 & -\frac{1}{3} & \frac{2}{3} & -\frac{1}{3} \end{bmatrix}$

Now use the 1 in the to eliminate the the -2 and 5 above it

According to the answer I'm given, the final matrix is:

[9/2 -1 1]
[-1 1 0]
[-2 2 -1]

How do you get that? If you've already figured out the bottom line to be [-1/3 2/3 -1/3]
That's why I'm so confused, I can't get that answer.
• May 5th 2011, 07:44 AM
TheEmptySet
Go back and double check your computations. You didn't post any work just where you were when you got stuck to I don't know where you went wrong.
Personally I find it better to just start over and be really careful with your row operations.