Cem Hayes

2020-12-28

Explain the concept of Inverse Matrices?

odgovoreh

Expert

Step 1
The inverse of a matrix X is a matrix such that when we multiply the matrix X by its inverse the result is the identity matrix. The symbol that we use to denote for the inverse matrix for
That is $X{X}^{-1}={X}^{-1}X=1$
There are two conditions for a matrix to have inverse.
(1) The matrix should be a square matrix.
(2) The determinant of the matrix should be non-zero $|X|\ne 0$
Step 2
The matrix which are not square matrix do not have the inverse.
A matrix which has inverse it also known as invertible matrix.
Here we can see as an example how to find inverse of a matrix
Let us consider a matrix
$X=\left(\begin{array}{cc}a& b\\ c& d\end{array}\right)$
$|X|=\left(ac-bd\right)$
$|X|=\left(ac-bd\right)\ne 0$
${X}^{-1}=\frac{1}{|X|}\left(\begin{array}{cc}d& -b\\ -c& a\end{array}\right)$
${X}^{-1}=\frac{1}{\left(ac-bd\right)}\left(\begin{array}{cc}d& -b\\ -c& a\end{array}\right)$

Jeffrey Jordon

Expert