Can't get inverse matrix with email transformations?

Question

Mathematics

-4 1 -2
5 -3 3
7 -3 -1
What am I doing wrong
UPG: Matrix :
-4 1 -2
5-3 -4
7 -3 -1

Answer 1

You are not doing something at all.
In order to find the inverse matrix by the method of equivalent transformations, you need to write the matrix itself, and next to it is the identity matrix of the same dimension. Further, making equivalent transformations, it is necessary to "exchange" these matrices in places. As a result, you will have the identity matrix on the left, and the inverse on the right.
First, using the Gaussian method, we reduce the matrix to a stepped form.

/ X X X  | 1 0 0 \
| 0 X X  | 0 1 0 |
\ 0 0 X  | 0 0 1 /

Then we multiply each row of the matrix by such a number that the diagonal of the left matrix consists of only ones.

/ 1 X X  | X X X \
| 0 1 X  | X X X |
\ 0 0 1  | X X X /

We bring the left matrix to a stepped form only already "from the bottom up".

/ 1 0 0  | X X X \
| 0 1 0  | X X X |
\ 0 0 1  | X X X /

The right matrix is ​​now inverse.
In general, I advise you to use another method for finding the inverse matrix (the one with algebraic additions), in which the probability of making an error is less.