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

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Answer 1 · 2016-11-02T23:55:43

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

Expanding using row1 we have;

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

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

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