How do you find the value of the determinant #|(6, 3, -1), (0, 3, 3), (-9, 0, 0)|#?

1 Answer
Jan 7, 2017

Answer:

#abs((6, 3, -1),(0, 3, 3),(-9,0,0)) = -108#

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 #"row2"# from #"row1"# to get:

#abs((6, 0, -4),(0, 3, 3),(-9,0,0))#

Add #3/2 xx "row1"# to #"row3"# to get:

#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#