Guassian elimination and Inverse Matrix

[phantomAI]

I'm still having trouble with Guassian elimination and finding the Inverse of a Matrix. I tend to get confused with the switching of the rows or factoring out something.

Example matrix

1 1 1 | 1
1 1 -2 | 3
2 1 1 | 2

so it's a system of linear equations and I must solve for x, y, and z.

I was wondering is someone could help show the steps in solving these matrices as well as explain finding the solution to the inverse matrix.

I know that to find the inverse, the Matrix must be dotted by the Identity matrix.

Thanks

 

[phantomAI]

never mind, I figured out how to do the inverse, but had to see it through a 2x2 matrix first. I'm still bad at doing the Guassian elimination matrix though unless I write out as a linear system of equations, but I don't want to keep on converting it to a linear system to solve..I just want to solve through matrix form.

 

[JJKorman1]

Gaussian Elimination & Matrix Inverse

The basic process is to hold the first row first column element constant while getting the 1st col, 2nd & 3rd to zero. Remembering to join a matrix of the same dimension (n*n) as an adjoint i.e. n*2n cols. The goal: shift the three right columns to the left by repeating the process in the first sentence, only in the second column the middle integer is reduced to 1 while the numbers above and below are reduced to 0.

This is fairly simple on a three by three matrix, gets trickier the higher one goes i.e. 5*5. At times there is no inverse so don't chase for a no answer situation. Solutions of inverses can be found on the Web using Google.

 

[philosophking]

May I ask how to find solutions on google? I'm still trying to figure out all of the wonderful aspects of the google calculator :). Thanks.