Question

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

Answer 1

Olá, Bruno.

$A=B^t\Leftrightarrow\left[\begin{array}{ccc}3&1\\4&-2\end{array}\right] =\left[\begin{array}{ccc}x+y&1\\x-y&-2\end{array}\right] \Leftrightarrow \begin{cases} x+y=3\\ x-y=4 \end{cases}(+)\Rightarrow\\\\\\ 2x=7\Rightarrow \boxed{x=\frac72}\Rightarrow \frac72+y=3\Rightarrow y=\frac62-\frac72\Rightarrow \boxed{y=-\frac12}$