Explain the concept of Inverse Matrices?

Question

odgovoreh · Accepted Answer

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

X is X^{- 1}

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 | \neq 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 = (\begin{matrix} a & b \\ c & d \end{matrix})

| X | = (a c - b d)

| X | = (a c - b d) \neq 0

X^{- 1} = \frac{1}{| X |} (\begin{matrix} d & - b \\ - c & a \end{matrix})

X^{- 1} = \frac{1}{(a c - b d)} (\begin{matrix} d & - b \\ - c & a \end{matrix})

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Explain the concept of Inverse Matrices?

Answered question

Answer & Explanation

New Questions in Precalculus