Question

Cum pot sa rezolv punctul b. la aceasta matrice ?

Answer 1

Uite, sper ca ai înțeles.

Answer 2

$\displaystyle A= \left(\begin{array}{ccc}1&2\\3&4\\\end{array}\right),~B= \left(\begin{array}{ccc}4&3\\2&1\\\end{array}\right),~C= \left(\begin{array}{ccc}1&1\\1&1\\\end{array}\right) \\ \\ a).det~A=-2 \\ \\ det~A= \left|\begin{array}{ccc}1&2\\3&4\\\end{array}\right|=1 \cdot 4-2 \cdot 3=4-6=-2 \Rightarrow det~A=-2$
$\displaystyle b).A+B=5C \\ \\ A+B= \left(\begin{array}{ccc}1&2\\3&4\\\end{array}\right)+ \left(\begin{array}{ccc}4&3\\2&1\\\end{array}\right)= \left(\begin{array}{ccc}1+4&2+3\\3+2&4+1\\\end{array}\right)= \left(\begin{array}{ccc}5&5\\5&5\\\end{array}\right) \\ \\ 5C=5 \cdot \left(\begin{array}{ccc}1&1\\1&1\\\end{array}\right)= \left(\begin{array}{ccc}5 \cdot 1&5 \cdot 1\\5 \cdot 1&5 \cdot 1\\\end{array}\right)= \left(\begin{array}{ccc}5&5\\5&5\\\end{array}\right)$
$\displaystyle A+B= \left(\begin{array}{ccc}5&5\\5&5\\\end{array}\right),~5C= \left(\begin{array}{ccc}5&5\\5&5\\\end{array}\right) \\ \\ \left(\begin{array}{ccc}5&5\\5&5\\\end{array}\right)= \left(\begin{array}{ccc}5&5\\5&5\\\end{array}\right) \Rightarrow A+B=5C$