Multiplication of Matrices

Published on: Fri Jan 23 2009

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. Reasoning: Observing the matrices shows p to be equal, giving us an m x n matrix of 2x1 [2 x 3][3x1] = [2x1] lin1.gif 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.