A soma dos elementos da matriz dada por [tex]f\left(\left[\begin{array}{cc}1&2\\1&0\end{array}\right]\right)[/tex] é C) 6.
Para encontrar a respostas, devemos calcular a matriz que resulta do cálculo de [tex]f\left(\left[\begin{array}{cc}1&2\\1&0\end{array}\right]\right)[/tex].
Para isso, temos que:
[tex]f(X) = X^2 + 2I\cdot X - C\\I = \left[\begin{array}{cc}1&0\\0&1\end{array}\right] \\C = \left[\begin{array}{cc}1&3\\2&4\end{array}\right][/tex]
Calculando X²:
[tex]X^2 = \left[\begin{array}{cc}1&2\\1&0\end{array}\right]\cdot \left[\begin{array}{cc}1&2\\1&0\end{array}\right] = \left[\begin{array}{cc}1\cdot 1+2\cdot 1&1\cdot 2+2\cdot 0\\1\cdot 1+0\cdot 1&1\cdot 2+0\cdot 0\end{array}\right]= \left[\begin{array}{cc}3&2\\1&2\end{array}\right][/tex]
Calculando 2I·X:
[tex]2\cdot I\cdot X = 2\cdot \left[\begin{array}{cc}1&0\\0&1\end{array}\right]\cdot \left[\begin{array}{cc}1&2\\1&0\end{array}\right] = 2\cdot\left[\begin{array}{cc}1\cdot 1+0\cdot 1&1\cdot 2+0\cdot 0\\0\cdot 1+1\cdot 1&0\cdot 2+1\cdot 0\end{array}\right]= \left[\begin{array}{cc}2&4\\2&0\end{array}\right][/tex]
Calculando f(X), temos:
[tex]f\left(\left[\begin{array}{cc}1&2\\1&0\end{array}\right]\right)=\left[\begin{array}{cc}3&2\\1&2\end{array}\right]+\left[\begin{array}{cc}2&4\\2&0\end{array}\right]-\left[\begin{array}{cc}1&3\\2&4\end{array}\right]=\left[\begin{array}{cc}4&3\\1&-2\end{array}\right][/tex]
Somando os elementos, encontramos:
4 + 3 + 1 - 2 = 6
Resposta: C
