Find the product of the following question.
A=( 1 2 3 4) B = ( 1 2 3
( 5 6 7 8 ) ( 4 5 6
( 7 8 9
( 10 11 12 )
Given,
A=(123 456 789)A = \begin{pmatrix}1&2&3\\ \:\:\:4&5&6\\ \:\:\:7&8&9\end{pmatrix}A=⎝⎛147258369⎠⎞ and B=(123 456 789)B = \begin{pmatrix}1&2&3\\ \:\:\:4&5&6\\ \:\:\:7&8&9\end{pmatrix}B=⎝⎛147258369⎠⎞
Then,
AB=(123 456 789)(123 456 789)AB = \begin{pmatrix}1&2&3\\ \:\:\:4&5&6\\ \:\:\:7&8&9\end{pmatrix} \begin{pmatrix}1&2&3\\ \:\:\:4&5&6\\ \:\:\:7&8&9\end{pmatrix}AB=⎝⎛147258369⎠⎞⎝⎛147258369⎠⎞
=(1⋅ 1+2⋅ 4+3⋅ 71⋅ 2+2⋅ 5+3⋅ 81⋅ 3+2⋅ 6+3⋅ 94⋅ 1+5⋅ 4+6⋅ 74⋅ 2+5⋅ 5+6⋅ 84⋅ 3+5⋅ 6+6⋅ 97⋅ 1+8⋅ 4+9⋅ 77⋅ 2+8⋅ 5+9⋅ 87⋅ 3+8⋅ 6+9⋅ 9)=\begin{pmatrix}1\cdot \:1+2\cdot \:4+3\cdot \:7&1\cdot \:2+2\cdot \:5+3\cdot \:8&1\cdot \:3+2\cdot \:6+3\cdot \:9\\ 4\cdot \:1+5\cdot \:4+6\cdot \:7&4\cdot \:2+5\cdot \:5+6\cdot \:8&4\cdot \:3+5\cdot \:6+6\cdot \:9\\ 7\cdot \:1+8\cdot \:4+9\cdot \:7&7\cdot \:2+8\cdot \:5+9\cdot \:8&7\cdot \:3+8\cdot \:6+9\cdot \:9\end{pmatrix}=⎝⎛1⋅1+2⋅4+3⋅74⋅1+5⋅4+6⋅77⋅1+8⋅4+9⋅71⋅2+2⋅5+3⋅84⋅2+5⋅5+6⋅87⋅2+8⋅5+9⋅81⋅3+2⋅6+3⋅94⋅3+5⋅6+6⋅97⋅3+8⋅6+9⋅9⎠⎞
AB=(303642668196102126150)AB=\begin{pmatrix}30&36&42\\ 66&81&96\\ 102&126&150\end{pmatrix}AB=⎝⎛306610236811264296150⎠⎞
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