How can I find the inverse of this matrix using any method?

[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

 

[Hurkyl]

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.

/  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.

 

[HallsofIvy]

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

 

[HallsofIvy]

Actually, I found the determinant by entering the matrix into my TI-89 calculator!