Look carefully and you’ll see the row by column multiplication, an essential
feature of matrix multiplication. If in addition to the unit profits we are given the
unit volumes 7 , 4 , 1 , 5 of each unit of the products, in one fell swoop we can
calculate the profits and storage requirements for the three factories by the single
matrix multiplication:
The total storage is provided by the second column of the resulting matrix,
that is 74, 54 and 39. Matrix theory is very powerful. Imagine the situation of a
company with hundreds of factories, thousands of products, and different unit
profits and storage requirements in different weeks. With matrix algebra the
calculations, and our understanding, are fairly immediate, without having to
worry about the details which are all taken care of.
Matrix algebra vs ordinary algebra
There are many parallels to be drawn between matrix algebra and ordinary
algebra. The most celebrated difference occurs in the multiplication of matrices.
If we multiply matrix A with matrix B and then try it the other way round:
So in matrix algebra we may have A × B and B × A being different, a situation