Thread: 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!

multiply row three by



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

Originally Posted by TheEmptySet

multiply row three by



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

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]



Now if you use






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

Originally Posted by TheEmptySet

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



Now if you use





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.

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.