How do you find the adjoint of a 3x3 matrix? can u explain example?

[mr_coffee]

Hello everyone, I think i don't understand the inverses because i don't understand how u find the adjoint of a nxn matrix. The book has this example and i have no idea how they got from A to A adj, makes no sense to me!

Here is the picture:
http://img89.imageshack.us/img89/3010/lastscan0oo.jpg
if that link is slow try:L
http://show.imagehosting.us/show/806170/0/nouser_806/T0_-1_806170.jpg
thanks!

 

[GDogg]

Hello everyone, I think i don't understand the inverses because i don't understand how u find the adjoint of a nxn matrix. The book has this example and i have no idea how they got from A to A adj, makes no sense to me!
Here is the picture:
http://img89.imageshack.us/img89/3010/lastscan0oo.jpg
if that link is slow try:L
http://show.imagehosting.us/show/806170/0/nouser_806/T0_-1_806170.jpg
thanks!

To find the adjoint of a A:

$$adj(A)_{ij} = (-1)^{i+j} det[A(j|i)]$$

That means that the entry in the row $$i$$ and column $$j$$ of $$adj(A)$$ is obtained by deleting the column $$j$$ and the row $$i$$ of A and then taking the determinant of that and multipliying by $$(-1)^{i+j}$$

For instance if u have a 3x3 matrix:
http://en.wikipedia.org/math/e36e0138b126ebbcf8fe80cd4f58f3aa.png

this is the adjoint:
http://en.wikipedia.org/math/a3c81ad8680add569a7377cda2529147.png

 

[mr_coffee]

Ahh thank u so much!