How do you find the determinant of #((2, -3, 5), (0, 1, -3), (0, 0, 2))#?
The determinant is
Since this is an upper triangular matrix, there is a theorem in linear algebra which states that its determinant is the product of the entries on the main diagonal.
We may verify this by performing co-factor expansion along any row or column of our choice.
Since row 3 contains 2 zero entries, we may use co-factor expansion along row 3 to obtain the determinant as
You may also view the link below to another similar problem of this nature that I solved in full detail previously for a student: