Question

M(a)= matrice(2a 0 mai jos 0 2a ) nu pot scrie matricea , aratati ca M(1/2)+M(-1/2)

Answer 1

[tex]M(a) = \left[\begin{array}{cc}2a&0\\0&2a\end{array}\right]\\ M(\frac{1}{2}) + M(-\frac{1}{2}) = \\= \left[\begin{array}{cc}2*\frac{1}{2}&0\\0&2*\frac{1}{2}\end{array}\right] + \left[\begin{array}{cc}2*(-\frac{1}{2})&0\\0&2*(-\frac{1}{2})\end{array}\right] = \\ = \left[\begin{array}{cc}1&0\\0&1\end{array}\right] + \left[\begin{array}{cc}-1&0\\0&-1\end{array}\right] = \\ = \left[\begin{array}{cc}0&0\\0&0\end{array}\right] = O_2\\[/tex]