Prentice Hall Algebra 2

12-2 Matrix Multiplication

Objective

To multiply matrices using scalar and matrix multiplication

A solve it problem with Tyler.
Image Long Description

In the Solve It, you may have found the sum of products. Finding the sum of products is essential to matrix multiplication.

Essential Understanding The product of two matrices is a matrix. To find an element in the product matrix, you multiply the elements of a row from the first matrix by the corresponding elements of a column from the second matrix. Then add the products.

Before you learn how to multiply two matrices, however, you should learn a simpler type of multiplication. This type of multiplication allows you to scale, or resize, the elements of the matrix.

table with 1 row and 5 columns , row1 column 1 , 3 . matrix with 2 rows and 2 columns , row1 column 1 , 5 , column 2 negative 1 , row2 column 1 , 3 , column 2 7 , end matrix , column 2 equals , column 3 . matrix with 2 rows and 2 columns , row1 column 1 , 3 open 5 close , column 2 3 open negative 1 close , row2 column 1 , 3 open 3 close , column 2 3 open 7 close , end matrix , column 4 equals , column 5 . matrix with 2 rows and 2 columns , row1 column 1 , 15 , column 2 negative 3 , row2 column 1 , 9 , column 2 21 , end matrix , end table

The real number factor (such as 3 in the example) is a scalar. Multiplication of a matrix A by a scalar c is scalar multiplication. To find the resulting matrix cA, you multiply each element of A by c.


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Table of Contents

Prentice Hall Algebra 2 Chapter 1 Expressions, Equations, and Inequalities Chapter 2 Functions, Equations, and Graphs Chapter 3 Linear Systems Chapter 4 Quadratic Functions and Equations Chapter 5 Polynomials and Polynomial Functions Chapter 6 Radical Functions and Rational Exponents Chapter 7 Exponential and Logarithmic Functions Chapter 8 Rational Functions Chapter 9 Sequences and Series Chapter 10 Quadratic Relations and Conic Sections Chapter 11 Probability and Statistics Chapter 12 Matrices Chapter 13 Periodic Functions and Trigonometry Chapter 14 Trigonometric Identities and Equations Skills Handbook English/Spanish Illustrated Glossary Selected Answers Index Acknowledgments