The method of find inverse matrix by elementary transformation by which method
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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 row by a constant
2) Adding a multiple of another row
3) Swapping two rows
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 1 or a 0, 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 top row into:
⎡⎣⎢1a21a310a22a320a23a33⎤⎦⎥
Then do the second row and then the third?
We can use three transformations:-
1) Multiplying a row by a constant
2) Adding a multiple of another row
3) Swapping two rows
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 1 or a 0, 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 top row into:
⎡⎣⎢1a21a310a22a320a23a33⎤⎦⎥
Then do the second row and then the third?
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