Somme et produit de matrices

Durée : 10 mn

Note maximale : 10

Question

\(A=\left[\begin{array}{c c c}2&3&5\\1&0&1\\2&1&0\end{array}\right]\) \(B=\left[\begin{array}{c c c}1&2\\1&0\\0&1\end{array}\right]\) \(C=\left[\begin{array}{c c c}2&3&1&4\\4&0&0&2\\1&0&1&0\end{array}\right]\)

\(D=\left[\begin{array}{c c c}2&0\\6&1\\0&1\end{array}\right]\) \(E=\left[\begin{array}{c c c}4&2&1\\1&1&1\end{array}\right]\) \(F=\left[\begin{array}{c c c}1&0&1&1\\0&1&1&1\\1&1&0&1\end{array}\right]\)

Effectuer les opérations suivantes si elles ont un sens :

\(\begin{array}{cccccc}B+D\\AB\end{array}\) \(\begin{array}{cccccc}C-2F\\BA\end{array}\) \(\begin{array}{cccccc}A+B\\BE\end{array}\) \(\begin{array}{cccccc}C-B\\EB\end{array}\) \(\begin{array}{cccccc}A^2\\CF\end{array}\) \(\begin{array}{cccccc}B^2\\CD\end{array}\) \(\begin{array}{cccccc}F^2\\DC\end{array}\) \(\begin{array}{cccccc}&\\BF\end{array}\)

Solution

\(A+B, C-B, B^2, F^2, BA, CF, CD, DC, BF\) n'ont pas de sens.

\(B+D=\left[\begin{array}{c c c}3&2\\7&1\\0&2\end{array}\right]\) \(C-2F=\left[\begin{array}{c c c}0&3&-1&2\\4&-2&-2&0\\-1&-2&1&-2\end{array}\right]\) \(A^2=\left[\begin{array}{c c c}17&11&13\\4&4&5\\5&6&11\end{array}\right]\)

\(AB=\left[\begin{array}{c c c}5&9\\1&3\\3&4\end{array}\right]\) \(BE=\left[\begin{array}{c c c}6&4&3\\4&2&1\\1&1&1\end{array}\right]\) \(EB=\left[\begin{array}{c c c}6&9\\2&3\end{array}\right]\)