help

[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.

[mmwave]

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]

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

[mmwave]

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]

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