# Math Help - Inverse matrix

1. ## Inverse matrix

Find the inverse of the matrix

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

Thanks!

2. also
if you take the matrix A and use a sequence of row operations to reduce it to I
then those same operations applied to I will give you A inverse

since you're basically doing (P1)(P2)...(Pn)A = I
which implies (P1)(P2)...(Pn) = A^-1

an easy way to do this is to take [A|I] and reduce the left part to I
what remains on the right will be A inverse

example:
1 1
0 1

you take
1 1 1 0
0 1 0 1

then your row operations to reduce the left part into I is simply R1-R2
==>
1 0 1 -1
0 1 0 1
so the inverse is
1 -1
0 1

now you can do it for the larger matrix

3. "Online Matrix Calculator"

Thank you for that! Now, I'm on an old computer, so the instructions doesn't show up. But if I did it right, the inverse of the matrix should be:

-1 0 0 0
0 -1 3/2 0
0 0 1/2 0
-3/2 3/2 -3/2 1/2

Is this right?

4. Originally Posted by gralla55
"Online Matrix Calculator"

Thank you for that! Now, I'm on an old computer, so the instructions doesn't show up. But if I did it right, the inverse of the matrix should be:

-1 0 0 0
0 -1 3/2 0
0 0 1/2 0
-3/2 3/2 -3/2 1/2

Is this right?
Yes, it's correct. I used Matlab and ended up with the same answer as you.

Code:
A =

-1     0     0     0
0    -1     3     0
0     0     2     0
-3     3    -3     2

EDU>> inv(A)

ans =

-1.0000         0         0         0
0   -1.0000    1.5000         0
0         0    0.5000         0
-1.5000    1.5000   -1.5000    0.5000