While using the elementary transformation method to find the inverse of a matrix, our goal is to convert the given matrix into an identity matrix.
We can use three transformations:- 1) Multiplying a column by a constant 2) Adding a multiple of another column 3) Swapping two column
The thing is, I can't seem to figure out what to do to achieve that identity matrix. There are so many steps which I can start off with, but how do I know which one to do? I think of one step to get a certain position to a 11 or a 00, and then get a new matrix. Now again there are so many options, it's boggling.
Is there some specific procedure to be followed? Like, first convert the first column into:
1 a12 a13
0 a22 a23 0 a32 a33
Then do the second column and then the third?
What do I start off with? I hope I've made my question clear enough.