Question

dadas as matrizes A=(2..0..1) e B=(1..4..0) determine a determinante do produto a^t.B
.....................................(3..2.-3).........(2..-1..1)

Answer 1

Olá!

Sejam as matrizes:

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

e

$B= \left[\begin{array}{ccc}1&4&0\\2&-1&1\end{array}\right]$

Portanto:

 $\det (A^t \cdot B) = \det \left( \left[\begin{array}{cc}2&3\\0&2\\1&-3\end{array}\right] \cdot \left[\begin{array}{ccc}1&4&0\\2&-1&1\end{array}\right] \right)\\ \det (A^t \cdot B) = \det \left( \left[\begin{array}{ccc}8&5&3\\4&-2&2\\-5&7&-3\end{array}\right] \right)$

Aplicando a Regra de Sarrus:

$\det (A^t \cdot B) = 48-50+84-30-112+60\\ \det (A^t \cdot B) = 0$

;)