How do you find the determinant of #((3, -3, 3), (1, -2, -1), (2, 0, 6))#?

1 Answer
Steve M
Nov 7, 2016

# |(3, -3, 3), (1, -2, -1), (2, 0 , 6)| = 0 #

Explanation:

Expanding using row1 we have;

# |(3, -3, 3), (1, -2, -1), (2, 0 , 6)| = (3)|(-2, -1), (0 , 6)| - (-3)|(1,-1), (2, 6)| + (3)|(1, -2), (2,0)| #

# = (3){(-2)(6)-(0)(-1)} + (3){(1)(6)-(2)(-1)} + (3){(1)(0)-(2)(-2)} #
# = (3)(-12) + (3)(6+2) + (3)(0-(-4)) #
# = -36 + (3)(8) + 12 #
# = -36 + 24 + 12 #
# = 0 #

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