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))#?
Multiply the diagonal to get:
The determinant of an upper or lower triangular matrix is just the product of the diagonal.
In this case
The determinant is
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: