Holt McDougal Algebra 1 10-Ext Matrices 10-Ext Matrices Holt Algebra 1 Lesson Presentation Lesson Presentation Holt McDougal Algebra 1

10-Ext Matrices Organize data in a matrix. Add and subtract matrices and multiply a matrix by a scalar. Objectives

Holt McDougal Algebra 1 10-Ext Matrices matrix entry scalar Vocabulary

Holt McDougal Algebra 1 10-Ext Matrices A matrix is a rectangular arrangement of numbers in rows and columns. Each number in the matrix is called an entry.

Holt McDougal Algebra 1 10-Ext Matrices Matrices are described by the number of rows and columns in the matrix. Matrix A is called a 3 × 2 (3 by 2) matrix because it has 3 rows and 2 columns. Matrix B contains the same data, but it is arranged in 2 rows and 3 columns, so it is called a 2 × 3 (2 by 3) matrix.

Holt McDougal Algebra 1 10-Ext Matrices Example 1: Organizing Data in a Matrix The table shows the number of yearbooks sold to students at two high schools. Arrange the data in a matrix. Give the dimensions of the matrix. 9th10th11th12th West Hills College Park Matrix The matrix has 2 rows and 4 columns, so its dimensions are 2 x 4.

Holt McDougal Algebra 1 10-Ext Matrices Check It Out! Example 1 The table shows the number of members in each section of two marching bands. Use this information to make a 3 x 2 matrix. PercussionBrassWoodwinds Northmount High Western High To make a matrix with 3 rows and 2 columns, have the rows represent the types of instruments and the columns represent the schools.

Holt McDougal Algebra 1 10-Ext Matrices If two matrices have the same dimensions, they can be added or subtracted by finding the sum or difference of the corresponding entries.

Holt McDougal Algebra 1 10-Ext Matrices Example 2A: Adding and Subtracting Matrices The matrices show the sales, in thousands of dollars, of two companies for the first three months of each year. Add the two matrices to find company A’s total sales, in thousands of dollars, for March.

Holt McDougal Algebra 1 10-Ext Matrices Example 2A Continued Add the two matrices to find company A’s total sales, in thousands of dollars, for March. The sales for Company A in March totaled $165,000.

Holt McDougal Algebra 1 10-Ext Matrices Subtract the two matrices to find by how many thousands of dollars February’s sales declined for Company B in year 2. The February sales for Company B declined $7,000 in year 2. Example 2B: Adding and Subtracting Matrices

Holt McDougal Algebra 1 10-Ext Matrices Check It Out! Example 2A The matrices show the enrollment by grade level at two high schools during the same year. What was the total enrollment of boys in the twelfth grade that year?

Holt McDougal Algebra 1 10-Ext Matrices Check It Out! Example 2A Continued What was the total enrollment of boys in the twelfth grade? The total enrollment of boys in the twelfth grade was 217.

Holt McDougal Algebra 1 10-Ext Matrices Check It Out! Example 2B The matrices show the enrollment by grade level at two high schools during the same year. How many more tenth-grade girls were enrolled at Washington High than at Central High that year?

Holt McDougal Algebra 1 10-Ext Matrices Check It Out! Example 2B Continued How many more tenth-grade girls were enrolled at Washington High than at Central High that year? There were 21 more tenth-grade girls enrolled at Washington High than at Central High.

Holt McDougal Algebra 1 10-Ext Matrices To multiply a matrix by a number, multiply each entry in the matrix by the number. This kind of multiplication is called scalar multiplication. The scalar is the number by which the matrix is multiplied.

Holt McDougal Algebra 1 10-Ext Matrices The matrices show the sales, by age, at two movie theaters. Ticket prices are going to increase by 25%. Multiply the matrix by 1.25 to show the new ticket prices. Example 3: Scalar Multiplication of a Matrix

Holt McDougal Algebra 1 10-Ext Matrices Example 3 Continued Multiply each entry in the matrix by the scalar x The scalar product shows the new ticket prices.

Holt McDougal Algebra 1 10-Ext Matrices The matrix shows the number of short sleeve and long sleeve T-shirts a store has in its inventory. A second store has 3 times as many shirts in inventory. How many of each shirt and size does the second store have in its inventory? Check It Out! Example 3

Holt McDougal Algebra 1 10-Ext Matrices Check It Out! Example 3A Continued Multiply each entry in the matrix by the scalar 3. The scalar product shows the number of shirts at the second store.