Question

Linear algebra

Can someone please help me with this thing:

https://www.dropbox.com/s/5n3c79khodit174/Screenshot%202016-03-15%2020.49.12.png?dl=0

Answer 1

@hartnn @phi @Kainui

Answer 2

mods are usually pretty busy xD and they are not the only ones that can help! lets try some other people @rebeccaxhawaii @imqwerty

Answer 3

can you type it out its not letting me view it

Answer 4

Adjoint of a matrix is basically the transpose of the cofactor elements in a matrix. Adjoint of a matrix can be easily used to compute the inverse of a matrix
\[\frac{adj(A)_{i,j}}{\det(A)} = A^{-1}\]

Answer 5

If A = 2x2 matrix defined as below

\[\left[\begin{matrix}a & b \\ c & d\end{matrix}\right] = A\]

Then
\[adj(A)_{i,j} = \left[\begin{matrix}d & -b \\ -c & a\end{matrix}\right]\]

Answer 6

But how would I go aobut defining the general element of the adjoint of any size matrix ?

Answer 7

@thushananth01

Answer 8

Have a look at this

Answer 9

is it true that (adj(A)ij = Cji

Answer 10

@thusjananth01

Answer 11

Yes C represents the cofactor

Answer 12

Maybe this lecture helps
http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-3-matrices/

the inverse is discussed at 38min, 30 sec