How do you find the determinant of #((1, 2, 3), (4, 5, 6), (7, 8, 9))#?
The determinant is
Since column 3 of the given matrix consists of numbers which are all constant multiples of each other, there is a theorem which states that the determinant of this matrix is
However, I will prove it from calculation just to verify and show how you would calculate such determinants should you not be aware of the theorems of linear matrix algebra.
Use co-factor expansion along any row or column of your choice.
This involves adding the products of the entries in each row with their co-factors
In this case, since the given matrix is
I will take co-factor expansion along row 1 as an example to find the determinant of the given matrix as :