How do you find the determinant of # ((5, 1, 4), (-1, f, e), (g, 0 , 1))#?

1 Answer
Steve M
Nov 2, 2016

# |(5, 1, 4), (-1, f, e), (g, 0 , 1)| = 5f+e+g-4fg #

Explanation:

Expanding using row1 we have;

# |(5, 1, 4), (-1, f, e), (g, 0 , 1)| = (5)|(f, e), (0 , 1)| - (1)|(-1,1), (g, e)| + (4)|(-1, f), (g,0)| #

# = (5){(f)(1)-(0)(e)} - (1){(-1)(e)-(g)(1)} + (4){(-1)(0)-(g)(f)} #
# = (5)(f) - (1)(-e-g) + (4)(-fg) #
# = 5f+e+g-4fg #

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