Pré-Vestibular ⇒ (MACKENZIE) Matriz Transposta Soma Tópico resolvido

[paulomm]

Se [tex3]\begin{pmatrix}
a & 2 \\
3 & y \\
\end{pmatrix}=\begin{pmatrix}
1 & b \\
x & 4 \\
\end{pmatrix}[/tex3] e [tex3]A =\begin{pmatrix}
a & b \\
x & y \\
\end{pmatrix}[/tex3]
e [tex3]B=A^{t}[/tex3] então Det. (AB) vale?

a) [tex3]8[/tex3]
b) [tex3]4[/tex3]
c) [tex3]2[/tex3]
d) [tex3]-2[/tex3]
e) [tex3]-4[/tex3]

[PedroCunha]

Veja:

[tex3]\circ \begin{pmatrix}a & 2 \\ 3 & y \\ \end{pmatrix} = \begin{pmatrix}1 & b \\ x & 4 \\ \end{pmatrix} \rightarrow a = 1, b = 2, x =3, y =4 \\\\
\circ A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \\\\
\circ B = \begin{pmatrix} 1 & 3 \\ 2 & 4 \end{pmatrix} \\\\
\circ AB = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \cdot \begin{pmatrix} 1 & 3 \\ 2 & 4 \end{pmatrix} \therefore AB = \begin{pmatrix} 5 & 11 \\ 11 & 25 \end{pmatrix} \\\\

\circ \det(AB) = 25 \cdot 5 - 11^2 \therefore \det(AB) = 125 - 121 \therefore \boxed{\boxed{\det(AB) = 4 }}[/tex3]

Penso que seja isso.

Att.,
Pedro