Question

Question:-

${\rm{ii)}}{\bigg(\begin{bmatrix} 0 & 1& 5\\ 0& 0 & 1\\ 9 & 3& 1 \\ \end{bmatrix} \bigg) \: \times \: \bigg(\begin{bmatrix} 6 & 1& 5\\ 0& 2 & 1\\ 4& 0& 2 \\ \end{bmatrix} \bigg)}$

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Answer 1

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

Given multiplication of matrices as

$\rm :\longmapsto\:{\begin{bmatrix} 0 & 1& 5\\ 0& 0 & 1\\ 9 & 3& 1 \\ \end{bmatrix} \: \times \: \begin{bmatrix} 6 & 1& 5\\ 0& 2 & 1\\ 4& 0& 2 \\ \end{bmatrix} }$

$\rm \:  =  \: \begin{bmatrix} 0 + 0 + 20 & 0 + 2 + 0& 0 + 1 + 10\\ 0 + 0 + 4& 0 + 0 + 0& 0 + 0 + 2\\ 0 + 0 + 4& 0 + 6 + 0& 0 + 3 + 2 \\ \end{bmatrix}$

$\rm \:  =  \: \begin{bmatrix} 20 & 2& 11\\ 4& 0 & 2\\ 4& 6& 5 \\ \end{bmatrix}$

Hence,

$\boxed{\tt{ \rm \: {\begin{bmatrix} 0 & 1& 5\\ 0& 0 & 1\\ 9 & 3& 1 \\ \end{bmatrix} \: \times \:\begin{bmatrix} 6 & 1& 5\\ 0& 2 & 1\\ 4& 0& 2 \\ \end{bmatrix}} =  \: \begin{bmatrix} 20 & 2& 11\\ 4& 0 & 2\\ 4& 6& 5 \\ \end{bmatrix}}}$

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MORE TO KNOW

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

2. Matrix multiplication is Commutative. i.e AB = BA

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

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

5. There exist an identity matrix I such that AI = IA = A

Answer 2

Question:-

${\rm{}}{\bigg(\begin{bmatrix} 0 & 1& 5\\ 0& 0 & 1\\ 9 & 3& 1 \\ \end{bmatrix} \bigg) \: \times \: \bigg(\begin{bmatrix} 6 & 1& 5\\ 0& 2 & 1\\ 4& 0& 2 \\ \end{bmatrix} \bigg)}$

Given:-

${\rm{}}{\bigg(\begin{bmatrix} 0 & 1& 5\\ 0& 0 & 1\\ 9 & 3& 1 \\ \end{bmatrix} \bigg) \: \times \: \bigg(\begin{bmatrix} 6 & 1& 5\\ 0& 2 & 1\\ 4& 0& 2 \\ \end{bmatrix} \bigg)}$

To Find:-

• Need to solve the Given Matrixes.

Solution:-

$\longmapsto{\rm{}}{\begin{bmatrix} 0 & 1& 5\\ 0& 0 & 1\\ 9 & 3& 1 \\ \end{bmatrix} \: \times \: \begin{bmatrix} 6 & 1& 5\\ 0& 2 & 1\\ 4& 0& 2 \\ \end{bmatrix} }$

Multiplication of the Given Matrixes.

$\begin{gathered}\rm \:  =  \: \begin{bmatrix} 0 \times 6 + 1 \times 0 + 5 \times 4&& 1 \times0 + 1 \times 2 + 5 \times 0 && 0 \times 5 + 1 \times 1 + 5 \times 2\\ 0 \times 6 + 0 \times 0 + 1 \times 4&& 0 \times 1 + 0 + 0&& 0 + 0 + 2\\ 0 + 0 + 4&& 0 + 6 + 0&& 0 + 3 + 2 \\ \end{bmatrix}\end{gathered}$

[tex] = \left[

\begin{array}{c c c} \sf

20& \sf 2 & \sf11 \\

\sf 4 & \sf0& \sf 2\\

\sf4 & \sf 6 & \sf5

\end{array}

\right] [/tex]

Answer:-

[tex] \red{ \boxed{{\rm{}}{\begin{bmatrix} 0 & 1& 5\\ 0& 0 & 1\\ 9 & 3& 1 \\ \end{bmatrix} \: \times \: \begin{bmatrix} 6 & 1& 5\\ 0& 2 & 1\\ 4& 0& 2 \\ \end{bmatrix} }= \left[

\begin{array}{c c c} \sf

20& \sf 2 & \sf11 \\

\sf 4 & \sf0& \sf 2\\

\sf4 & \sf 6 & \sf5

\end{array}

\right]}}[/tex]

Hope you have satisfied. ⚘