How do you find the determinant of #|(3,4), (2,5)|#?

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Answer 1 · 2017-01-18T12:38:22

# det ( (3,4), (2,5) ) = 7#

The use of proper notation should be observed, as:

# |(3,4), (2,5)| " "#, or # " "det ( (3,4), (2,5) )#

is the determinant, and you cannot find the determinant of a determinant. The question should be, find the determinant of

# ( (3,4), (2,5) ) #

Which is a 2x2 matrix. The determinant of a 2x2 matrix can be calculated as follows:

# det ( (a,b), (c,d) ) = |(a,b), (c,d)| = ad-bc #

Hence:

# det ( (3,4), (2,5) ) = |(3,4), (2,5)| #
#" " = (3)(5) - (2)(4) #
#" " = 15 - 8 #
#" " = 7 #