Linear Algebra: Finding the Inverse of a Matrix

[LaraCroft]

Linear algebra question...

Hello again!

Ok...so if I let A =

[0 1 0 ]
[1 1 -2]
[2 3 -3]

How would I find A^-1? Is that the notation for inverse?

Also, could I express A^-1 as a product of at most five elementary matrices? What does this mean exactly?

Thanks!

 

[lurflurf]

Elementary matrices are the representation of elementary operations. So see if you can get from the identity to A with five or fewer operations. Hint may help to instead see if you can go from A to I in five steps.

Elementary operations are
-interchange two rows
-multiply a row by a nonzero value
-add a multiple of a row to another

 

[HallsofIvy]

Use row reduction to reduce A to the identity matrix. The elementary matrices corresponding to those row operations will multiply to give A^-1.