How do you find the value of the determinant #|(4, 1, 0), (5, -15, -1), (-2, 10, 7)|#?

1 Answer
Steve M
Jan 19, 2017

#|(4, 1, 0), (5, -15, -1), (-2, 10 , 7)| = -413#

Explanation:

Expanding using row1 we have;

# |(4, 1, 0), (5, -15, -1), (-2, 10 , 7)| = (4)|(-15, -1), (10 , 7)| - (1)|(5,-1), (-2, 7)| + (0)|(5, -15), (-2,10)| #

# = (4){(-15)(7)-(10)(-1)} - (1){(5)(7)-(-2)(-1)} #
# = (4)(-105+10) - (1)(35-2) #
# = (4)(-95)-33 #
# = -380-33 #
# = -413 #

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