Question

Vă rog frumos să rezolvați ex 11​

Answer 1

Răspuns:

Explicație pas cu pas:

Answer 2

Explicație pas cu pas:

$A \times B = \left(\begin{array}{ccc}5&3\\3&2\end{array}\right) \times \left(\begin{array}{ccc}2&-3\\-3&5\end{array}\right) =$

$= \left(\begin{array}{ccc}5 \times 2 + 3( - 3)&5( - 3) + 3 \times 5\\3 \times 2 + 2( - 3)&3( - 3) + 2 \times 5\end{array}\right)$

$= \left(\begin{array}{ccc}10 - 9& - 15 + 15\\6 - 6& - 9 + 10\end{array}\right) = \left(\begin{array}{ccc}1&0\\0&1\end{array}\right) = I_{2}$

$B \times A = \left(\begin{array}{ccc}2&-3\\-3&5\end{array}\right) \times \left(\begin{array}{ccc}5&3\\3&2\end{array}\right) =$

$= \left(\begin{array}{ccc}2 \times 5 + ( - 3) \times 3&2 \times 3 + ( - 3) \times 2\\( - 3) \times 5 + 5 \times 3& ( - 3) \times 3 + 5 \times 2\end{array}\right)$

$= \left(\begin{array}{ccc}10 - 9&6 - 6\\ - 15 + 15& - 9 + 10\end{array}\right) = \left(\begin{array}{ccc}1&0\\0&1\end{array}\right) = I_{2}$

$A \times B = B \times A = I_{2}$

q.e.d.