CHAPTER 03.13: BINARY OPERATIONS:
Rules of binary matrix operations Part 3 of 4 In
this segment we’ll talk about some rules of binary matrix operations. So
let’s talk about the associative law of multiplication. And what is the association
law of multiplication? That let there be an A matrix and let’s suppose this
is M rows and n columns. Then B is n rows and p columns and C then has p rows
and let’s suppose R columns. So we have three matrices, M rows and N columns,
N rows and P columns and P rows and R columns. So the number of columns here
are the same as the number of rows here, and the number of columns here is
the same as the number of rows here. So be three matrices. Then in that case
what’s going to happen is that if I take A times B times C here like this,
what b times C has done first then its multiplied to A, will be same as multiplying
A by B then multiplying by C. So
if we look at the association law of multiplication and say that hey let me
go and do the B times C first, and then ill multiply it to A. And you’ll find
out that it will turn out to be the same matrix as if you were going to
multiply B by A and then multiply it by C. And these orders are extremely
important because you can very well see that if this is M by N and this is N
by P and this is P by R, only then we’ll find out that hey these matrix
multiplications are valid. Same thing here - this M by N here, N by P here,
and P by R here, only then those matrix multiplications are valid. And then
the resulting matrix will be M rows and R columns. So if we call this to be,
let’s suppose D, to be A times B times C, then because this is M rows and N
columns, this is N rows and P columns and this is P rows and R columns. This
resulting matrix D will have this many rows and this many columns. And that
is the associative law of multiplication. And that is the end of this
segment. |