I was stuck in understanding how to go from the second to third step of finding eigenvectors. Your third equation and explanation have help me immensely. I'm still a work in progress, but I may have crossed the Rubicon, thanks to you.
It's very simple, the idea is to reduce the augmented matrix into it's row echelon form, that way because we have a 2*2 matrix, the a21 value needs to be zero. So based on the elements in Row 1 we perform elementary row operations to get a zero for a21.
