Question

Daca AB=BA,aratati că det B mai mic sau egal cu 0. Matricele A= (1 2 4 1)
B=(0 x y 0)
HELPPP!!

Answer 1

[tex] \left(\begin{array}{cc}1&2\\4&1\end{array}\right)\cdot \left(\begin{array}{cc}0&x\\y&0\end{array}\right)=\left(\begin{array}{cc}0&x\\y&0\end{array}\right) \cdot \left(\begin{array}{cc}1&2\\4&1\end{array}\right)\\ 2y=4x=\ \textgreater \ y=2x\\ detB=-xy=-2x^2\leq0[/tex]