Question

1)     Dadas as matrizes A =$<var>\left[\begin{array}{ccc}3&1\\4&-2\end{array}\right]</var>$ e B = $<var>\left[\begin{array}{ccc}x + y&x - y\\1&-2\end{array}\right]</var>$ , determine x e y para que A = Bt.

Answer 1

Olá, Meirelles.

$B^t= \left[\begin{array}{cc}x+y&1\\x-y&-2\end{array}\right] \\\\\\ A=B^t\Leftrightarrow \begin{cases}3=x+y\\1=1\\4=x-y\\-2=-2\end{cases}\Leftrightarrow \begin{cases}x+y=3\\x-y=-4\end{cases} \\\\\ \text{Somando as duas equa\c{c}\~oes, temos:}\\\\ 2x=-1\Rightarrow \boxed{x=-\frac12}\Rightarrow -\frac12+y=3\Rightarrow y=3+\frac12\\\\\\\boxed{y=\frac72}$