Answer to Question #180106 in Linear Algebra for Oliver

Question

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 )

Answer 1

Given,

$A = \begin{pmatrix}1&2&3\\ \:\:\:4&5&6\\ \:\:\:7&8&9\end{pmatrix}$ and $B = \begin{pmatrix}1&2&3\\ \:\:\:4&5&6\\ \:\:\:7&8&9\end{pmatrix}$

Then,

$AB = \begin{pmatrix}1&2&3\\ \:\:\:4&5&6\\ \:\:\:7&8&9\end{pmatrix} \begin{pmatrix}1&2&3\\ \:\:\:4&5&6\\ \:\:\:7&8&9\end{pmatrix}$

$=\begin{pmatrix}1\cdot \:1+2\cdot \:4+3\cdot \:7&1\cdot \:2+2\cdot \:5+3\cdot \:8&1\cdot \:3+2\cdot \:6+3\cdot \:9\\ 4\cdot \:1+5\cdot \:4+6\cdot \:7&4\cdot \:2+5\cdot \:5+6\cdot \:8&4\cdot \:3+5\cdot \:6+6\cdot \:9\\ 7\cdot \:1+8\cdot \:4+9\cdot \:7&7\cdot \:2+8\cdot \:5+9\cdot \:8&7\cdot \:3+8\cdot \:6+9\cdot \:9\end{pmatrix}$

$AB=\begin{pmatrix}30&36&42\\ 66&81&96\\ 102&126&150\end{pmatrix}$