SOLUTION: Find the inverse(if it exists) 1 0 1 1 1 -3 0 1 -3 i don't know how to solve a 3x3 if you can please explain

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Question 126342: Find the inverse(if it exists)
1 0 1
1 1 -3
0 1 -3
i don't know how to solve a 3x3 if you can please explain
Answer by solver91311(12126) About Me  (Show Source):
You can put this solution on YOUR website!
For an n X n matrix, create an n X 2n matrix by adding n columns consisting of the n X n identity matrix.

Your problem:
A=%28matrix%283%2C3%2C%0D%0A1%2C0%2C1%2C%0D%0A1%2C1%2C-3%2C%0D%0A0%2C1%2C-3%29%29

The 3 X 3 Identity matrix:
%28matrix%283%2C3%2C%0D%0A1%2C0%2C0%2C%0D%0A0%2C1%2C0%2C%0D%0A0%2C0%2C1%29%29

Putting them together in a 3 X 6 matrix:
%28matrix%283%2C6%2C%0D%0A1%2C+0%2C+1%2C+1%2C+0%2C+0%2C%0D%0A1%2C+1%2C-3%2C+0%2C+1%2C+0%2C%0D%0A0%2C+1%2C-3%2C+0%2C+0%2C+1%29%0D%0A%29

Now, perform row reduction operations until the matrix is completely reduced, if possible.
R2+=+R2+-+R1
%28matrix%283%2C6%2C%0D%0A1%2C+0%2C+1%2C+1%2C+0%2C+0%2C%0D%0A0%2C+1%2C-4%2C-1%2C+1%2C+0%2C%0D%0A0%2C+1%2C-3%2C+0%2C+0%2C+1%29%0D%0A%29


R3+=+R3+-+R2
%28matrix%283%2C6%2C%0D%0A1%2C+0%2C+1%2C+1%2C+0%2C+0%2C%0D%0A0%2C+1%2C-4%2C-1%2C+1%2C+0%2C%0D%0A0%2C+0%2C+1%2C+1%2C-1%2C+1%29%0D%0A%29

R1+=+R1+-+R3
%28matrix%283%2C6%2C%0D%0A1%2C+0%2C+0%2C+0%2C+1%2C-1%2C%0D%0A0%2C+1%2C-4%2C-1%2C+1%2C+0%2C%0D%0A0%2C+0%2C+1%2C+1%2C-1%2C+1%29%0D%0A%29

R2+=+R2+%2B+4R3
%28matrix%283%2C6%2C%0D%0A1%2C+0%2C+0%2C+0%2C+1%2C-1%2C%0D%0A0%2C+1%2C+0%2C+3%2C-3%2C+4%2C%0D%0A0%2C+0%2C+1%2C+1%2C-1%2C+1%29%0D%0A%29

Hence:
A%5E%28-1%29=%28matrix%283%2C3%2C%0D%0A0%2C+1%2C-1%2C%0D%0A3%2C-3%2C+4%2C%0D%0A1%2C-1%2C+1%29%0D%0A%29