Stitz-Zeager_College_Algebra_e-book

This demonstrates the utility of using row operations

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 1 2 −8 2 0 −1 8 −5 9 A= B= 4 −10 3 5 5 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

Ask a homework question - tutors are online