Matrix multiplication, the very first structure should have a number of columns equivalent to the 2nd composite row figures, and the further calculation can be defined as follows:
Given :
[tex]\bold{[ 4, 1, 2] \times \left[\begin{array}{ccc}4&3&2\\1&5&3\\1&3&6\end{array}\right] }[/tex]
To find:
multiplication=?
Solution:
- If the column is one = the row in the other, matrix and vector can be multiplied.
- The vector of multiplication (1 row, three columns) with a matrix of (3 rows, 3 columns) will be magnified by increasing a production company matrix of (1 row and three columns).
[tex]\to \bold{[ 4, 1, 2] \times \left[\begin{array}{ccc}4&3&2\\1&5&3\\1&3&6\end{array}\right] }[/tex]
[tex]= [ (4)(4) + (1)(3) + (2)(2) \ \ \ \ \ \ \ \ (4)(1) + (1)(5) + (2)(3) \ \ \ \ \ \ \ (4)(1) + (1)(3) + (2)(6) ]\\\\= [ 16 + 3 + 4 \ \ \ \ \ \ \ \ \ \ \ 4 + 5 + 6 \ \ \ \ \ \ \ \ \ \ \ 4 + 3 + 8 ]\\\\= [ 23 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 15 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 15 ]\\\\[/tex]
So, the multiplication "[tex][23\ \ \ 15 \ \ \ 15][/tex]".
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