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

Jan 19, 2017

$| \left(4 , 1 , 0\right) , \left(5 , - 15 , - 1\right) , \left(- 2 , 10 , 7\right) | = - 413$

#### Explanation:

Expanding using row1 we have;

$| \left(4 , 1 , 0\right) , \left(5 , - 15 , - 1\right) , \left(- 2 , 10 , 7\right) | = \left(4\right) | \left(- 15 , - 1\right) , \left(10 , 7\right) | - \left(1\right) | \left(5 , - 1\right) , \left(- 2 , 7\right) | + \left(0\right) | \left(5 , - 15\right) , \left(- 2 , 10\right) |$

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