# How do you find the determinant of #((1, 0, 0, 0), (sqrt3, 2, 0, 0), (-0.003, 0, -3, 0), (1.432, sqrt37, pi, 1))#?

##### 2 Answers

Mar 28, 2016

Multiply the diagonal to get:

#### Explanation:

The determinant of an upper or lower triangular matrix is just the product of the diagonal.

In this case

Mar 28, 2016

The determinant is

#### Explanation:

Since this is a lower triangular matrix, there is a theorem in linear algebra which says that is determinant is the product of entries on the main diagonal

To verify this, use the method of co-factor expansion along row 1 since it contains the most zeroes.

For a full example of how to work out a matrix with more non-zero entries, see this link to a similar question:

https://socratic.org/questions/how-do-you-find-the-determinant-of-1-2-3-4-5-6-7-8-9#245541