Question

Daca matricea A=( 1 -2) atunci (A+3*i2)*A=? Ma puteti ajuta si sa imi dati cateva
(3 -4) explicatii?

Answer 1

$A = \left(\begin{array}{cc}1&-2\\3&-4\end{array}\right) \\ \\ (A+3I_{2})\cdot A =\left[\left(\begin{array}{cc}1&-2\\3&-4\end{array}\right)+3\cdot \left(\begin{array}{cc}1&0\\0&1\end{array}\right)\right]\cdot \left(\begin{array}{cc}1&-2\\3&-4\end{array}\right) \\ \\ =\left[\left(\begin{array}{cc}1&-2\\3&-4\end{array}\right)+\left(\begin{array}{cc}3&0\\0&3\end{array}\right)\right]\cdot \left(\begin{array}{cc}1&-2\\3&-4\end{array}\right)\\ \\ =\left(\begin{array}{cc}1+3&-2+0\\3+0&-4+3\end{array}\right)\cdot \left(\begin{array}{cc}1&-2\\3&-4\end{array}\right) \\ \\ = \left(\begin{array}{cc}4&-2\\3&-1\end{array}\right)\cdot \left(\begin{array}{cc}1&-2\\3&-4\end{array}\right)\\ \\ = \left(\begin{array}{cc}4\cdot 1+(-2)\cdot 3&4\cdot (-2)+(-2)\cdot (-4)\\3\cdot 1+(-1)\cdot 3&3\cdot(-2)+(-1)\cdot (-4)\end{array}\right)\\ \\=\left(\begin{array}{cc}4-6&-8+8\\3-3&-6+4\end{array}\right) \\ \\= \left(\begin{array}{cc}-2&0\\0&-2\end{array}\right) =\\ \\ = -2I_{2}$