# Determine the inverse

tony blair
Could someone show me how to determine the inverse to this
Any method

A solution today would be great!!

A= 2 1 -3 1
-3 -2 0 2
2 1 0 -1
1 0 1 2

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## Answers and Replies

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Hurkyl
Staff Emeritus
Gold Member
step one: enter the matrix into mathematica...

er... jk.

I presume you know how to do row reduction in the context of solving equations right?

The work done in inverting a matrix is the same as in solving a system of equations. You first adjoin an identity matrix to your matrix (instead of adjoining a single column). e.g.

Code:
/  2  1 -3  1 |  1  0  0  0 \
| -3 -2  0  2 |  0  1  0  0 |
|  2  1  0 -1 |  0  0  1  0 |
\  1  0  1  2 |  0  0  0  1 /
Now, you row reduce your original matrix, just like you would when solving a system of equations. You have to fully row reduce it so the left hand matrix has a diagonal of all 1's and 0's everywhere else (iow you can't partially reduce it). Then, the right hand matrix will be the inverse you were trying to compute.

If you are going to do row reduction by hand on a 4x4 matrix or larger always check that the determinant is not zero before you start. If it is zero, there is no inverse to the matrix.

HallsofIvy
Homework Helper
But the simplest way to find the determinant of a large matrix is row reduction!

Originally posted by HallsofIvy
But the simplest way to find the determinant of a large matrix is row reduction!
Nah, the simplest way is det(A) in Matlab.

HallsofIvy