How do you find the determinant of ((2, -3, 5), (0, 1, -3), (0, 0, 2))?

Mar 27, 2016

The determinant is $4$.

Explanation:

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

$\Delta = 2 {\left(- 1\right)}^{3 + 3} | \left(1 , - 3\right) , \left(0 , 2\right) | = 2 \left(2\right) = 4$.

You may also view the link below to another similar problem of this nature that I solved in full detail previously for a student:
https://socratic.org/questions/how-do-you-find-the-determinant-of-1-2-3-4-5-6-7-8-9#245541