# Determinants

## Determinant

The determinant is essentially a way to find out if the columns of the matrix, ie the spanning vectors of the column space are linearly dependent or not. If the determinant of the matrix is zero, it essentially means that the columns are linearly dependent.&#x20;

It is also a way of telling if the systems of eqns will have infinitely many solutions or be unique, if they have infinitely many solutions that means that determinant is zero.&#x20;

* Matrix with determinant zero is called singular matrix.
* Determinant of upper or lower triangular matrix is given by multiplication of diagonal entries of the matrix.&#x20;
* [https://youtu.be/OIEEt8SuQYk?list=PLlXfTHzgMRULWJYthculb2QWEiZOkwTSU](https://youtu.be/OIEEt8SuQYk?list=PLlXfTHzgMRULWJYthculb2QWEiZOkwTSU)

There is a geometrical analogous of determinant as well. The determinant in 2D gives area of paralellogram given by the columns of matrix and in 3D gives volume. &#x20;
