dada as matrizes a=[2002] e b=[3003] determine a matriz x, tal que x=a.bt + b.

\(A = \{\begin{matrix} 2 & 0 \\ 0 & 2 \end{matrix} \} \\ B = \{\begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix} \} \\ B^t = \{\begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix} \}\)

Logo, a matriz X pedida será:

\(X = \{\begin{matrix} 2 & 0 \\ 0 & 2 \end{matrix} \} \{\begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix} \} + \{\begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix} \} \\ X = \{\begin{matrix} 6 & 0 \\ 0 & 6 \end{matrix} \} + \{\begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix} \} \\ \boxed{X = \{\begin{matrix} 9 & 0 \\ 0 & 9 \end{matrix} \}}\)