# How do you find the determinant of |(1.5, -3.6, 2.3), (4.3, 0.5, 2.2), (-1.6, 8.2, 6.6)|?

Dec 20, 2016

The answer is $= 175.668$

#### Explanation:

The determinant is calculated as follows

$| \left(a , b , c\right) , \left(d , e , f\right) , \left(g , h , i\right) |$

$= a | \left(e , f\right) , \left(h , i\right) | - b | \left(d , f\right) , \left(g , i\right) | + c | \left(d , e\right) , \left(g , h\right) |$

$= a \left(e i - f h\right) - b \left(\mathrm{di} - f g\right) + c \left(\mathrm{dh} - e g\right)$

Therefore,

$| \left(1.5 , - 3.6 , 2.3\right) , \left(4.3 , 0.5 , 2.2\right) , \left(- 1.6 , 8.2 , 6.6\right) |$

$= 1.5 \left(6.6 \cdot 0.5 - 2.2 \cdot 8.2\right) + 3.6 \left(4.3 \cdot 6.6 + 2.2 \cdot 1.6\right) + 2.3 \left(4.3 \cdot 8.2 + 1.6 \cdot 0.5\right)$

$= - 22.1 + 114.84 + 82.938 = 175.668$