Question

determine o valor do determinante da Matriz A​

Answer 1

Resposta:

-345

Explicação passo a passo:

Podemos usar a regra de sarrus:

$\left[\begin{array}{ccc}2&-1&2\\5&9&5\\9&0&-6\end{array}\right]$

Vamos duplicar a 1°e 2° colunas

$\left[\begin{array}{ccc}2&-1&2\\5&9&5\\9&0&-6\end{array}\right]\left[\begin{array}{ccc}2&-1\\5&9\\9&0\end{array}\right]$

Multiplicaremos os termos partindo do a11 até o a31 da seguinte maneira:

$\left[\begin{array}{ccc}\boxed2&-1&2\\5&\boxed9&5\\9&0&\boxed{-6}\end{array}\right]\left[\begin{array}{ccc}2&-1\\5&9\\9&0\end{array}\right]$

2*9*(-6)=-108

$\left[\begin{array}{ccc}2&\boxed{-1}&2\\5&9&\boxed5\\\9&0&-6\end{array}\right]\left[\begin{array}{ccc}2&-1\\5&9\\\boxed9&0\end{array}\right]$

-1*5*9=-45

$\left[\begin{array}{ccc}2&-1&\boxed2\\5&9&5\\9&0&-6\end{array}\right]\left[\begin{array}{ccc}2&-1\\\boxed5&9\\9&\boxed0\end{array}\right]$

2*5*0=0

Somando todos esses termos:-108+(-45)-0=-153

Agora faremos ao contrário:

$\left[\begin{array}{ccc}2&-1&2\\5&9&5\\9&0&\boxed{-6}\end{array}\right]\left[\begin{array}{ccc}2&\boxed{-1}\\\boxed5&9\\9&0\end{array}\right]$

-1*5*(-6)=30

$\left[\begin{array}{ccc}2&-1&2\\5&9&\boxed5\\9&\boxed0&-6\end{array}\right]\left[\begin{array}{ccc}\boxed2&-1\\5&9\\9&0\end{array}\right]$

2*5*0=0

$\left[\begin{array}{ccc}2&-1&\boxed2\\5&\boxed9&5\\\boxed9&0&-6\end{array}\right]\left[\begin{array}{ccc}2&-1\\5&9\\9&0\end{array}\right]$

2*9*9=162

Agora subtraindo os termos:

-30-0-162=-192

Somando as duas partes: -192-153=-345