Question

Calcule o valor de X e Y respectivamente no sistema Linear abaixo ​

Answer 1

Resposta:

x-40 e y=10

Explicação passo a passo:

$\boxed{\left \{ {{x+y=50} \atop {x-y=30}} \right. }$

Temos a matriz

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

$B=\left[\begin{array}{ccc}50\\30\end{array}\right]$

Assim $X=A^{-1}B$

$\left[\begin{array}{ccc}1&1\\1&-1\end{array}\right] X=\left[\begin{array}{ccc}50\\30\end{array}\right]$

$X=\left[\begin{array}{ccc}\frac{1}{2} &\frac{1}{2}\\\frac{1}{2}&-\frac{1}{2}\end{array}\right] *\left[\begin{array}{ccc}50\\30\end{array}\right]=\left[\begin{array}{ccc}40 \\10\end{array}\right]$