Finding Inverse of A Matrix: Example A

[mrroboto]

How do you take the inverse of a matrix?

The specific example I have is

A=

1 1 1 1
1 1 1 3
1 1 3 3
1 3 3 3

Find A^-1

 

[cristo]

There are loads of ways. The quickest is probably to write the identity matrix to the right of A, and then to perform row operations such that the left hald becomes the identity. The matrix on the right is then the inverse.

 

[mrroboto]

what do you mean by "row operations?

so I take

1 1 1 1
1 1 1 3
1 1 3 3
1 3 3 3

and put

1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1

next to it...and then what? add? multiply?

 

[cristo]

Is this a homework problem? Are you in a linear algebra class? If so, you should have covered this; if not, then I presume you haven't studied linear algebra, so I'm not sure why you'd want to find this inverse.

 

[cristo]

Anyway, here's a link to an example on how to use this technique to find inverse matrices: http://www.sonoma.edu/users/w/wilsonst/Courses/Math_107/MT3/p10/inv/inv.html

 

[mrroboto]

Ok, I'll look.

 

[mrroboto]

Thanks. That was very helpful.

 

[copper-head]

This is quiet an easy thing to do. Row operations are many but the most basic ones are addition of two rows, substitution and multiplication by a scalar.
Your goal is to make look like
1111 1000
1113 0100
1133 0010
1333 0001
I would suggest that you subtract the first row from every other row making all elements in the first column underneath the first entry zeros.
Do the same for each column to reduce your matrix to row echelon form.
Remember to execute the same operations on your identity matrix as well!

Good luck.