Question

calcule o determinante!!!
socorro

Answer 1

Olá!

Letra a)

$a)~~ \left[\begin{array}{ccc}2&3&-4\\-2&1&2\\0&5&6\end{array}\right] \\ \\\\ \\ Det=\begin{array}{ccc}~~2&3&-4\\-2&1&~~2\\~~0&5&~~6\end{array}\begin{array}{ccc}~~2&3\\-2&1\\~~0&5\end{array}$

$Det=[(2*1*6)+(3*2*0)+(-4*-2*5)]~-~[(-4*1*0)+(2*2*5)+(3*-2*6)]\\ \\ Det=[12+0+40]~-~[0+20+(-36)]\\ \\ Det=52-(-16)\\ \\ Det=52+16\\ \\\\ \boxed{Det=68}$

Questão b)

$\left[\begin{array}{ccc}~~2&~~3&-1\\~~3&-1&~~1\\-1&~~0&~~3\end{array}\right] \\ \\\\ \\ Det=\begin{array}{ccc}~~~~~ 2&~~3&-1\\~~~~~3&-1&~~1\\~~-1&~~0&~~3\end{array}\begin{array}{ccc}-2&~~3\\~~3&-1\\-1&~~0\end{array}$

$Det=[(2*-1*3)+(3*1*-1)+(-1*3*0)]~-~[(-1*-1*-1)+(-2*1*0)+(3*3*3)]\\ \\ Det=[-6-3+0]~-~[-1+0+27]\\ \\ Det=-9-26\\ \\\\ \boxed{Det=-35}$

:)