Question

1. (FAAP) - São dadas as matrizes
A= [ ] B=(-11)
Calcular A.B + A-1.

Answer 1

$\boxed{\begin{array}{l}\sf A=\begin{bmatrix}\sf3&\sf2\\\sf7&\sf5\end{bmatrix}\\\sf det~A=15-14=1\\\sf Adj~A=\begin{bmatrix}\sf5&\sf-2\\\sf-7&\sf3\end{bmatrix}\\\sf A^{-1}=\dfrac{1}{det~A}\cdot adj~A\\\\\sf A^{-1}=\dfrac{1}{1}\cdot\begin{bmatrix}\sf5&\sf-2\\\sf-7&\sf3\end{bmatrix}\\\\\sf A^{-1}=\begin{bmatrix}\sf5&\sf-2\\\sf-7&\sf3\end{bmatrix}\end{array}}$

$\boxed{\begin{array}{l}\sf A\cdot B=\begin{bmatrix}\sf3\cdot1+2\cdot(-1)&\sf3\cdot1+2\cdot1\\\sf7\cdot1+5\cdot(-1)&\sf7\cdot1+5\cdot1\end{bmatrix}=\begin{bmatrix}\sf1&\sf5\\\sf2&\sf12\end{bmatrix}\\\sf A\cdot B+A^{-1}=\begin{bmatrix}\sf6&\sf3\\\sf-5&\sf15\end{bmatrix}\end{array}}$