Thread: 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!

Online Matrix Calculator

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

"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?

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