A practical example
Suppose the matrix A represents the output of the AJAX company in one
week. The AJAX company has three factories located in different parts of the
country and their output is measured in units (say 1000s of items) of the four
products it produces. In our example, the quantities, tallying with matrix A
opposite, are:
In the next week the production schedule might be different, but it could be
written as another matrix B. For example B might be given by
What is the total production for both weeks? The matrix theorist says it is the
matrix A + B where corresponding numbers are added together,
Easy enough. Sadly, matrix multiplication is less obvious. Returning to the
AJAX company, suppose the unit profit of its four products are 3 , 9 , 8 , 2. We
can certainly compute the overall profit for Factory 1 with outputs 7, 5, 0, 1 of its
four products. It works out as 7 × 3 + 5 × 9 + 0 × 8 + 1 × 2 = 68.
But instead of dealing with just one factory we can just as easily compute the
total profits T for all the factories