Question

does anyone know how to invert:

Answer 1

a 3x3 matrix
{-1 3 0 }
{ 1 -2 1 }
{ 0 1 2 }

Answer 2

The inverse of a mtrix is such that\[AA^-1 = I\]with I being the Identity

First calculate the determinant which in this case is -1.

Then find the determinants of all the smaller parts of the matrix, if the original matrix can be represented with each row being represented by the first number and the second number representing the column it will look like\[\left[\begin{matrix}1,1 & 1,2 & 1,3 \\ 2,1 & 2,2 & 2,3\\ 3,1 & 3,2 & 3,3\end{matrix}\right]\]We have to find the determinants of each smaller matrix and sub them in to our new inverse!

Are you with me so far?

Answer 3

http://mathworld.wolfram.com/MatrixInverse.html will tell you what order to do that in. The final answer that you should come up with is

Answer 4

A's our matrix
and A-1 is what we're trying to find
how does the determinant relate to the identity?

Answer 5

\[\left[\begin{matrix}5 & 6 & -3 \\ 2 & 2 & -1\\-1 & -1 & 1\end{matrix}\right]\]

Answer 6

The inverse is equal to 1/det(A) followed by big matrix stuff