Question

hi guys....can anyone please explain me how to find inverse of a matrix using elementary operations....with examples!! it will be a great help!!!
No junk answers allowed!!!

Answer 1

Hoooo..

Jiiiiiii....


This is a fun way to find the Inverse of a Matrix:

Play around with the rows (adding, multiplying or swapping) until we make Matrix A into the Identity Matrix I matrix A | I becomes I | A inverse And by ALSO doing the changes to an Identity Matrix it magically turns into the Inverse!
The "Elementary Row Operations" are simple things like adding rows, multiplying and swapping ... but let's see with an example:

Example: find the Inverse of "A":
matrix A

We start with the matrix A, and write it down with an Identity Matrix I next to it:

matrix A augmented
(This is called the "Augmented Matrix")

Identity Matrix
The "Identity Matrix" is the matrix equivalent of the number "1":

Identity Matrix
A 3x3 Identity Matrix
It is "square" (has same number of rows as columns),
It has 1s on the diagonal and 0s everywhere else.
It's symbol is the capital letter I.


Now we do our best to turn "A" (the Matrix on the left) into an Identity Matrix. The goal is to make Matrix A have 1s on the diagonal and 0s elsewhere (an Identity Matrix) ... and the right hand side comes along for the ride, with every operation being done on it as well...