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

um I dont knwo lolStep-by-step explanation:...

Q). If | 1 , 1, 3 | A = | 5, 2, 6 |, then find - id11352614508927, eliarnol9517

Ответ:

coolman5999alt

04.10.2021

Mathematics

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

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

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

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

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

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

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

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Learn More :-

Matrix multiplication is defined when number of columns of pre multiplier is equal to the number of rows of post multiplier.

Matrix multiplication may or may not be Commutative.

Matrix multiplication is Associative. i.e (AB)C = A(BC)

Matrix multiplication is Distributive. i.e. A ( B + C ) = AB + AC

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

Ответ:

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