Calculate the Inverse of a Matrix II
Inverse of a Matrix theory
Inverse of a Matrix
If the product between two matrices is the identity matrix, then we say that the matrices are “inverse”; because by multiplying them we obtain the neutral element for the product .
Consider the inverse matrix:
It must accomplish that: A · A-1 = I
Observe the following example.
So, we obtain the following equations system to get the inverse matrix values.
By applying this method we say that:
Where att (A)t is attached matrix and det (A) is the determinant of the matrix A.
The A determinant solution can be seen in the corresponding section about determinants theory.
att (A)t is obtained as follows:
Given matrix A:
Its attached is formed by the determinings which are result by suppressing a row and column of each of one of the elements.
For example, the a32 element position would be occupied by the determining which results by eliminating the third row and second column, that is:
and as the row + column (3+2) is odd we change the sign.
Then we perform its transpose:
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