Răspuns:
Explicație pas cu pas:
[tex]detA=\left|\begin{array}{ccc}1&0&-1\\2&1&0\\4&0&-2\end{array}\right|[/tex]
1 0 -1
2 1 0
detA=-2-(-4)=2
[tex]detB=\left|\begin{array}{ccc}1&2&3\\2&3&1\\3&1&2\end{array}\right|[/tex]
1 2 3
2 3 1
detB=6+6+6-(27+1+8)=18-36=-18
[tex]A\cdot B=\left(\begin{array}{ccc}1&0&-1\\2&1&0\\4&0&-2\end{array}\right)\cdot \left(\begin{array}{ccc}1&2&3\\2&3&1\\3&1&2\end{array}\right)=\left(\begin{array}{ccc}-2&1&1\\4&7&7\\-2&6&8\end{array}\right)[/tex]
[tex]det(A\cdot B)=\left|\begin{array}{ccc}-2&1&1\\4&7&7\\-2&6&8\end{array}\right|[/tex]
-2 1 1
4 7 7
det(A×B)=-112+24-14-(-14-112+32)=-8
detA×detB=2×(-18)=-36
[tex]A^2=\left(\begin{array}{ccc}1&0&-1\\2&1&0\\4&0&-2\end{array}\right)\cdot \left(\begin{array}{ccc}1&0&-1\\2&1&0\\4&0&-2\end{array}\right)=\left(\begin{array}{ccc}-3&0&1\\4&1&-2\\-4&0&0\end{array}\right)[/tex]
[tex]A^3=\left(\begin{array}{ccc}-3&0&1\\4&1&-2\\-4&0&0\end{array}\right)\cdot \left(\begin{array}{ccc}1&0&-1\\2&1&0\\4&0&-2\end{array}\right)=\left(\begin{array}{ccc}1&0&1\\-2&1&0\\-4&0&4\end{array}\right)[/tex]
[tex]detA^3=\left|\begin{array}{ccc}1&0&1\\-2&1&0\\-4&0&4\end{array}\right|[/tex]
1 0 1
-2 1 0
detA³=4-(-4)=8
(detA)³=2³=8
