Inverse matrix

• Feb 17th 2010, 04:36 PM
gralla55
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!
• Feb 17th 2010, 05:21 PM
pickslides
• Feb 17th 2010, 06:14 PM
jbpellerin
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
• Feb 18th 2010, 06:36 AM
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?
• Feb 18th 2010, 09:40 AM
Roam
Quote:

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```