Some basic terms:
Ith row and jth column
m row by n column matrix
When multiplying matrices multiply row by column.
Using a third variable p to describe the row or column in a pair of matrices to be multiplied
A = m x p
B = p x n
A(B) = m x n
So what I just said is that m rows by p columns when multiplied by a matrix which has an equal number of rows p as the columns of the original matrix, will give an answer of a matrix which has as many rows as matrix A and as many columns as matrix B.
So For example, we have two matrices. A and B
A has 3 rows and 2 columns
B has 2 rows and 4 columns.
We can multiply!
And the answer should have 2 rows and 4 columns. We can multiply if p is equal in both matrix A and B.
What happens if p is not equal in both matrices?
Then AB is undefined
Practice Problems from HotMath
Problem 19: Is the matrix product of the given matrices defined? If so, find it. If not, give reasons.
Observing the matrices shows p to be equal, giving us an m x n matrix of 2×1
[2 x 3][3×1] = [2×1]
So what exactly did I do?
First step was to lay the B matrix on it’s side to equal the number of rows in matrix A that is what gives me the 2 rows part. Since I have only one column to work with in B I only lay that column down, but if I had two columns I would have laid it down twice per row.
Then I drop the rows from matrix A down to match up.