Q). If | 1 , 1, 3 | A = | 5, 2, 6 |, then find A³ | -2, -1, -3 |

Mathematics

2 answers:

Anna007 [38]3 years ago

7 0

Answer:

A³ = [ 1, 1, 27, 125, 8, 216, -8, -1, -27].

Step-by-step explanation:

All the numbers in the bracket should be cubed.

I hope you understood ♥️♥️♥️

pishuonlain [190]3 years ago

3 0

Step-by-step explanation:

$\large\underline{\sf{Solution-}}$

Given matrix is

$\rm :\longmapsto\: \begin{gathered}\sf A=\left[\begin{array}{ccc}1&1&3\\5&2&6\\ - 2&-1& - 3\end{array}\right]\end{gathered}$

Consider,

$\red{\rm :\longmapsto\: {A}^{2}}$

$\rm \: = \: A \times A$

$\\ \rm \: = \: \begin{gathered}\sf \left[\begin{array}{ccc}1&1&3\\5&2&6\\ - 2&-1& - 3\end{array}\right]\end{gathered}\begin{gathered}\sf \left[\begin{array}{ccc}1&1&3\\5&2&6\\ - 2&-1& - 3\end{array}\right]\end{gathered} \\$

$\rm \: = \: \begin{gathered}\sf \left[\begin{array}{ccc}1 + 5 - 6&1 + 2 - 3&3 + 6 - 9\\5 + 10 - 12&5 + 4 - 6&15 + 12 - 18\\ - 2 - 5 + 6&-2 - 2 + 3& - 6 - 6 + 9\end{array}\right]\end{gathered}$

$\rm \: = \: \begin{gathered}\sf \left[\begin{array}{ccc}0&0&0\\3&3&9\\ - 1&-1& - 3\end{array}\right]\end{gathered}$

$\\ \bf\implies \: {A}^{2} = \begin{gathered}\sf \left[\begin{array}{ccc}0&0&0\\3&3&9\\ - 1&-1& - 3\end{array}\right]\end{gathered} \\$

Now, Consider

$\red{\rm :\longmapsto\: {A}^{3}}$

$\rm \: = \: {A}^{2} \times A$

$\\ \rm \: = \: \begin{gathered}\sf \left[\begin{array}{ccc}0&0&0\\3&3&9\\ - 1&-1& - 3\end{array}\right]\end{gathered} \times \begin{gathered}\sf \left[\begin{array}{ccc}1&1&3\\5&2&6\\ - 2&-1& - 3\end{array}\right]\end{gathered}$

$\\ \rm \: = \: \begin{gathered}\sf \left[\begin{array}{ccc}0&0&0\\3 + 15 - 18&3 + 6 - 9&9 + 18 - 27\\ - 1 - 5 + 6&-1 - 2 + 3& - 3 - 6 + 9\end{array}\right]\end{gathered} \\$