How do you find the determinant of #((1, 3, 5), (1, 1, 3), (2, 8, 12))#?

1 Answer
Steve M
Nov 3, 2016

# |(1, 3, 5), (1, 1, 3), (2, 8 , 12)| = 0 #

Explanation:

Expanding using row1 we have;

# |(1, 3, 5), (1, 1, 3), (2, 8 , 12)| = (1)|(1, 3), (8 , 12)| - (3)|(1,3), (2, 12)| + (5)|(1, 1), (2,8)| #

# = (1){(1)(12)-(8)(3)} - (3){(1)(12)-(2)(3)} + (5){(1)(8)-(2)(1)} #
# = (1)(12-24) - (3)(12-6) + (5)(8-2) #
# = (1)(-12) - (3)(6) + (5)(6) #
# = -12 - 18 + 30 #
# = 0 #

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