Question

Compute the entry (the number in the second row and second column) of the product matrix resulting from the following multiplication:

[1 2] [9 6]
[3 4] [5 7]

Answer 1

Answer:

The entry on the second row and second column of the product matrix is $c_{22} = 40$.

Step-by-step explanation:

Let's define as A and B the given matrixes:

$A = \left[\begin{array}{cc}1&2\\3&4\end{array}\right]$

$B = \left[\begin{array}{cc}9&6\\5&7\end{array}\right]$

The product matrix C entry in the first row and first column $c_{1,1}$ or $c_{11}$ can be computer multiplying first row of A by first column of B (see example attached).

The product matrix C entry in the first row and second column $c_{1,2}$ or $c_{12}$ can be computer multiplying first row of A by second column of B.

The product matrix C entry in the second row and first column $c_{2,1}$ or $c_{21}$ can be computer multiplying second row of A by first column of B.

The product matrix C entry in the second row and second column $c_{2,2}$ or $c_{22}$ can be computer multiplying second row of A by second column of B.

Then, let's compute $c_{22}$ by doing the dot product between [3 4] and [6 7]...

$c_{22} = [3 4] . [6 7] = 3*4 + 4*7 = 12 + 28 = 40$