Question

Rezolvațimi tema asta urgent

Answer 1

Răspuns:

31; 11; 83

Explicație pas cu pas:

$A - B = \left(\begin{array}{ccc}2&-1\\3&4\end{array}\right) - \left(\begin{array}{ccc}-3&2\\1&-1\end{array}\right) = \left(\begin{array}{ccc}2-(-3)&-1-2\\3-1&4-(-1)\end{array}\right) = \left(\begin{array}{ccc}5&-3\\2&5\end{array}\right)$

$det(A-B) = \left|\begin{array}{ccc}5&-3\\2&5\end{array}\right| = 5 \cdot 5 - 2 \cdot ( - 3) = 25 + 6 = \bf 31$

$AB = \left(\begin{array}{ccc}2&-1\\3&4\end{array}\right) \cdot \left(\begin{array}{ccc}-3&2\\1&-1\end{array}\right) = \left(\begin{array}{ccc}2 \cdot ( - 3) + ( - 1) \cdot 1&2 \cdot 2 + ( - 1) \cdot (-1)\\3( - 3) + 4 \cdot 1&3 \cdot 2 + 4 \cdot ( - 1)\end{array}\right) = \left(\begin{array}{ccc}-7&5\\-5&2\end{array}\right)$

$det(AB) = \left|\begin{array}{ccc}-7&5\\-5&2\end{array}\right| = - 7 \cdot 2 - ( - 5) \cdot 5 = - 14 + 25 = \bf 11$

$2A = 2\left(\begin{array}{ccc}2&-1\\3&4\end{array}\right) = \left(\begin{array}{ccc}2 \cdot 2&2 \cdot (-1)\\2 \cdot 3&2 \cdot 4\end{array}\right) = \left(\begin{array}{ccc}4&-2\\6&8\end{array}\right)$

$2A-B = \left(\begin{array}{ccc}4&-2\\6&8\end{array}\right) - \left(\begin{array}{ccc}-3&2\\1&-1\end{array}\right) = \left(\begin{array}{ccc}7&-4\\5&9\end{array}\right)$

$det(2A-B) = \left|\begin{array}{ccc}7&-4\\5&9\end{array}\right| = 7 \cdot 9 - 5 \cdot ( - 4) = 63 + 20 = \bf 83$