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Determine the inverse

  • Thread starter tony blair
  • Start date
  • #1
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
 
Last edited by a moderator:

Answers and Replies

  • #2
Hurkyl
Staff Emeritus
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step one: enter the matrix into mathematica...

er... jk. :smile:


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.
 
  • #3
211
2
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.
 
  • #4
HallsofIvy
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But the simplest way to find the determinant of a large matrix is row reduction!
 
  • #5
211
2
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. :wink:
 
  • #6
HallsofIvy
Science Advisor
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Actually, I found the determinant by entering the matrix into my TI-89 calculator!
 

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