Question

1. Sabendo que a inversa da matriz...
Determine x e y
Alguém pfv?

Answer 1

$\boxed{\begin{array}{l}\sf Se ~uma~matriz~\acute e~inversa~da~outra~ent\tilde ao~o~produto~delas\\\sf\acute e~igual~a~matriz~identidade.\end{array}}$

$\begin{bmatrix}\sf-2&\sf\dfrac{1}{2}\\\sf x&\sf1\end{bmatrix}\cdot\begin{bmatrix}\sf-\dfrac{1}{4}&\sf\dfrac{1}{8}\\\sf y&\sf\dfrac{1}{2}\end{bmatrix}=\begin{bmatrix}\sf1&\sf0\\\sf0&\sf1\end{bmatrix}$

$\begin{bmatrix}\sf\dfrac{1}{2}+\dfrac{y}{2}&\sf0\\\sf-\dfrac{1}{4}x+y&\sf\dfrac{1}{8}x+\dfrac{1}{2}\end{bmatrix}=\begin{bmatrix}\sf1&\sf0\\\sf0&\sf1\end{bmatrix}$

$\begin{cases}\sf\dfrac{1}{2}+\dfrac{1}{2}y=1\cdot2\\\sf-\dfrac{1}{4}x+y=0\end{cases}\\\begin{cases}\sf 1+y=2\\\sf y=\dfrac{1}{4}x\end{cases}\\\sf1+y=2\\\sf y=2-1\\\sf y=1\\\sf y=\dfrac{1}{4}x\implies x=4y\\\sf x=4\cdot1\\\sf x=4$