Question

me ajudem com essa matriz​

Answer 1

$\left[\begin{array}{ccc}1&4\\3&3\end{array}\right]~.~\left[\begin{array}{ccc}a\\b\end{array}\right]~~=~~\left[\begin{array}{ccc}6\\9\end{array}\right]\\\\\\\\\left[\begin{array}{ccc}1~.~a~+~4~.~b\\3~.~a~+~3~.~b\end{array}\right]~~=~~\left[\begin{array}{ccc}6\\9\end{array}\right]\\\\\\\\\left[\begin{array}{ccc}~a~+~4b\\3a~+~3b\end{array}\right]~~=~~\left[\begin{array}{ccc}6\\9\end{array}\right]$

Igualando as duas matrizes, chegamos ao sistema:

$\left\{\begin{array}{ccc}~a~+~4b~=~6\\3a~+~3b~=~9\end{array}\right\\\\\\\left\{\begin{array}{ccc}~a~+~4b~=~6\\a~+~b~=~3\end{array}\right\\\\\\Utilizando~o~metodo~da~adicao,~podemos~resolver~o~sistema~ \\fazendo~1^a~equacao-2^a~equacao:\\\\(a+4b)-(a+b)~=~6-3\\\\3b~=~3\\\\b~=~\frac{3}{3}\\\\\boxed{b~=~1}\\\\\\a+b~=~3\\\\a+1~=~3\\\\a~=~3-1\\\\\boxed{a~=~2}$