Adjoint, Inverse and Solving Equations

How determinants are used to find the inverse of a matrix and solve systems of linear equations.

Adjoint and Inverse

The inverse of a matrix (when it exists) is calculated as:

$$A^{-1} = \frac{1}{|A|} \, \text{adj}(A)$$

Note: A matrix has an inverse only if its determinant is non-zero (i.e. the matrix is non-singular).

A system of linear equations $AX = B$ can be solved using $X = A^{-1}B$, provided $A^{-1}$ exists.

Lesson 10 of 32