How do you find the value of the determinant #(6, 3, 1), (0, 3, 3), (9, 0, 0)#?
1 Answer
Jan 7, 2017
Explanation:
I will use a couple of properties of the determinant:

The determinant is unaltered when a multiple of one row is added to (or subtracted from) another row.

The determinant of an upper ot lower triangular matrix is the product of the main diagonal.
Given:
#abs((6, 3, 1),(0, 3, 3),(9,0,0))#
Subtract
#abs((6, 0, 4),(0, 3, 3),(9,0,0))#
Add
#abs((6, 0, 4),(0, 3, 3),(0,0,6))#
Since this is an upper triangular matrix, we can just multiply the diagonal to get the determinant:
#abs((color(blue)(6), 0, 4),(0, color(blue)(3), 3),(0,0,color(blue)(6))) = 6*3*(6) = 108#