Unformatted text preview: eﬁned, the number of entries in the rows of A
must match the number of entries in the columns of B . This means that the number of columns
of A must match the number of rows of B .7 In other words, to multiply A times B , the second
dimension of A must match the ﬁrst dimension of B , which is why in Deﬁnition 8.10, Am×n is being
multiplied by a matrix Bn×r . Furthermore, the product matrix AB has as many rows as A and as
many columns of B . As a result, when multiplying a matrix Am×n by a matrix Bn×r , the result is
the matrix ABm×r . Returning to our example matrices below, we see that A is a 2 × 3 matrix and
B is a 3 × 4 matrix. This means that the product matrix AB is deﬁned and will be a 2 × 4 matrix. 3
0 −2 −12
7 The reader is encouraged to think this through carefully. 8.3 Matrix Arithmetic 483 Using Ri to denote the ith row of A and Cj to denote the j th column of B , we form AB according
to Deﬁnition 8.10.
AB = R1 · C 1 R1 · C 2 R1 · C 3 R1 · C 4
R2 · C 1 R2 · C 2 R2 · C...
View Full Document