![\rm :\longmapsto\: \begin{gathered}\sf A=\left[\begin{array}{ccc}1&1&3\\5&2&6\\ - 2&-1& - 3\end{array}\right]\end{gathered}](/tpl/images/2490/2379/6658a.png)
![\\ \rm \: = \: \begin{gathered}\sf \left[\begin{array}{ccc}1&1&3\\5&2&6\\ - 2&-1& - 3\end{array}\right]\end{gathered}\begin{gathered}\sf \left[\begin{array}{ccc}1&1&3\\5&2&6\\ - 2&-1& - 3\end{array}\right]\end{gathered} \\](/tpl/images/2490/2379/9fe69.png)
![\rm \: = \: \begin{gathered}\sf \left[\begin{array}{ccc}1 + 5 - 6&1 + 2 - 3&3 + 6 - 9\\5 + 10 - 12&5 + 4 - 6&15 + 12 - 18\\ - 2 - 5 + 6&-2 - 2 + 3& - 6 - 6 + 9\end{array}\right]\end{gathered}](/tpl/images/2490/2379/8ffb3.png)
![\rm \: = \: \begin{gathered}\sf \left[\begin{array}{ccc}0&0&0\\3&3&9\\ - 1&-1& - 3\end{array}\right]\end{gathered}](/tpl/images/2490/2379/16051.png)
![\\ \bf\implies \: {A}^{2} = \begin{gathered}\sf \left[\begin{array}{ccc}0&0&0\\3&3&9\\ - 1&-1& - 3\end{array}\right]\end{gathered} \\](/tpl/images/2490/2379/40537.png)
![\\ \rm \: = \: \begin{gathered}\sf \left[\begin{array}{ccc}0&0&0\\3&3&9\\ - 1&-1& - 3\end{array}\right]\end{gathered} \times \begin{gathered}\sf \left[\begin{array}{ccc}1&1&3\\5&2&6\\ - 2&-1& - 3\end{array}\right]\end{gathered}](/tpl/images/2490/2379/71083.png)
![\\ \rm \: = \: \begin{gathered}\sf \left[\begin{array}{ccc}0&0&0\\3 + 15 - 18&3 + 6 - 9&9 + 18 - 27\\ - 1 - 5 + 6&-1 - 2 + 3& - 3 - 6 + 9\end{array}\right]\end{gathered} \\](/tpl/images/2490/2379/889b0.png)
![\\ \rm \: = \: \begin{gathered}\sf \left[\begin{array}{ccc}0&0&0\\0&0&0\\ 0&0&0\end{array}\right]\end{gathered}](/tpl/images/2490/2379/d0f56.png)
![\\ \bf\implies \: {A}^{3} = \: \begin{gathered}\sf \left[\begin{array}{ccc}0&0&0\\0&0&0\\ 0&0&0\end{array}\right]\end{gathered}](/tpl/images/2490/2379/8bf44.png)
Q). If
| 1 , 1, 3 |
A = | 5, 2, 6 |, then find A³
| -2, -1, -3 |
...
Mathematics, 04.10.2021 19:50 21vdawson
Q). If
| 1 , 1, 3 |
A = | 5, 2, 6 |, then find A³
| -2, -1, -3 |
Answers: 2
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