Question

Sendo A=|2 1| , qual a solucao da equação x+5A=A²+2I₂
               |1 3| ⇒ isso é uma matriz                                       
                           

Answer 1

Olá, Ivan.

$X+5A=A\²+2I_2\Rightarrow\\\\ X+5 \left[\begin{array}{cc} 2&1\\1&3\end{array}\right] =\left[\begin{array}{cc} 2&1\\1&3\end{array}\right] \cdot\left[\begin{array}{cc} 2&1\\1&3\end{array}\right] +2\left[\begin{array}{cc} 1&0\\0&1\end{array}\right] \Rightarrow\\\\ X+\left[\begin{array}{cc} 10&5\\5&15\end{array}\right] =\left[\begin{array}{cc} 5&5\\5&10\end{array}\right]+\left[\begin{array}{cc} 2&0\\0&2\end{array}\right] \Rightarrow$

$X=\left[\begin{array}{cc} 7&5\\5&12\end{array}\right]-\left[\begin{array}{cc} 10&5\\5&15\end{array}\right] \Rightarrow\\\\ X=\left[\begin{array}{cc} -3&0\\0&-3\end{array}\right]\Rightarrow\\\\ \boxed{X=-3I_2}$