3x3 Inverse Matrix
GarimaLunawat
Is there a formula for solving the inverse of a 3 by 3 matrix like there is an equation for the 2x2 matrix?
alexwang: May 4, 2015, 8:36 p.m.
I don't think so. For a 3x3 inverse matrix you need to augment the matrix by the identity matrix on the right side and row reduce to find your inverse matrix. Such as: 1 1 1 | 1 0 0 3 5 1 | 0 1 0 2 1 4 | 0 0 1
kelvincheng: May 4, 2015, 9:27 p.m.
According to Wikipedia, there is a formula for the inverse of a 3x3 matrix (that I have yet to verify for myself). http://en.wikipedia.org/wiki/Invertible_matrix#Inversion_of_3.C3.973_matrices Unlike the 2x2 formula, it's quite complicated. And I think for our purposes, it's easier to use the augmented matrix and row reduction like Alex said.
dannystapleton: May 4, 2015, 9:49 p.m.
Try doing #3 on the midterm practice. my Matrix for the 3x3: $\frac{2}{3}$ $\frac{-1}{2}$ $\frac{1}{3}$ $\frac{-8}{3}$ 2 $\frac{-1}{3}$ 1 $\frac{-1}{2}$ 0
dannystapleton: May 4, 2015, 9:51 p.m.
first three numbers make up column 1, second three make up column 2, last three make up column 3.
valerie: May 4, 2015, 10:12 p.m.
I got something close to that, but not exactly. I got 1 -1/2 1/3 -3 2 -1/3 1 -1/2 0
valerie: May 4, 2015, 10:25 p.m.
Found my mistake
danielkim: May 4, 2015, 10:50 p.m.
There is a method to find inverses of square matrices greater than 2x2, but for the sake of what we've learnt so far, it's best to place do this: Let A be an nxn square matrix A^-1 = [A|I] --> rref --> [I|A^-1]
ShengyueHuo: May 5, 2015, 9:25 p.m.
You can use [ A3 | I3 ]--> [ I3 | A^-1 ] to find the answer.