The table shows the top scores for girls in barrel racing at the 2004 National High School Rodeo finals. The data can be presented in a table or a spreadsheet as rows and columns of numbers. You can also use a matrix to show table data. A matrix is a rectangular array of numbers enclosed in brackets.

The dimensions of a matrix are determined by its number of rows and columns (in that order). Matrix A has dimensions 2  3. Each value in a matrix is called an entry of the matrix.

The address of an entry is its location in a matrix, expressed by using the lower case matrix letter with row and column number as subscripts. The score 16.206 is located in row 2 column 1, so a21 is 16.206.

Example 1: Displaying Data in Matrix Form The prices for different sandwiches are presented at right. 6 in 9 in Roast beef $3.95 $5.95 Turkey $3.75 $5.60 Tuna $3.50 $5.25 A. Display the data in matrix form. P = 3.95 5.95 3.75 5.60 3.50 5.25 B. What are the dimensions of P? P has three rows and two columns, so it is a 3  2 matrix.

Example 1: Displaying Data in Matrix Form Roast beef $3.95 $5.95 Turkey $3.75 $5.60 Tuna $3.50 $5.25 The prices for different sandwiches are presented at right. C. What is entry p12? What does is represent? The entry at p12, in row 1 column 2, is 5.95. It is the price of a 9 in. roast beef sandwich. D. What is the address of the entry 3.50? The entry 3.50 is at p31.

Use matrix M to answer the questions below. Check It Out! Example 1 Use matrix M to answer the questions below. a. What are the dimensions of M? 3  4 b. What is the entry at m32? 11 c. The entry 0 appears at what two addresses? m14 and m23

You can add or subtract two matrices if they have the exact same dimensions. Simply add or subtract the corresponding entries.

Example 2A: Finding Matrix Sums and Differences Add or subtract, if possible. 3 –2 1 0 4 7 2 5 1 –1 1 4 –2 3 2 –2 3 1 0 4 W = , X = , Y = , Z = W + Y Add each corresponding entry. 3 –2 1 0 + 1 4 –2 3 = 3 + 1 –2 + 4 1 + (–2) 0 + 3 4 2 –1 3 = W + Y =

Example 2B: Finding Matrix Sums and Differences Add or subtract, if possible. 3 –2 1 0 4 7 c a 1 –1 1 4 –2 3 b –2 3 1 0 4 W = , X = , Y = , Z = X – Z Subtract each corresponding entry. 4 7 c a 1 –1 b –2 3 1 0 4 – 4-b 9 c-3 a-1 1 –5 = X – Z =

Example 2C: Finding Matrix Sums and Differences Add or subtract if possible. 4 –2 –3 10 2 6 3 2 0 –9 –5 14 4 –1 –5 3 2 8 0 1 –3 3 0 10 A = , B = , C = , D = B – A B is a 2  3 matrix, and A is a 3  2 matrix. Because B and A do not have the same dimensions, they cannot be subtracted.

You can multiply a matrix by a number, called a scalar You can multiply a matrix by a number, called a scalar. To find the product of a scalar and a matrix, or the scalar product, multiply each entry by the scalar.

Check It Out! Example 4b 4 –2 –3 10 4 –1 –5 3 2 8 3 2 0 –9 D = [6 –3 8] A = B = C = Evaluate 2A – 3C, if possible. 4 –2 –3 10 = 2 – 3 3 2 0 –9 2(4) 2(–2) 2(–3) 2(10) = + –3(3) –3(2) –3(0) –3(–9) 8 –4 –6 20 = + –9 –6 0 27 = –1 –10 –6 47

Example 3: Business Application Use a scalar product to find the prices if a 10% discount is applied to the prices above. Shirt Prices T-shirt Sweatshirt Small $7.50 $15.00 Medium $8.00 $17.50 Large $9.00 $20.00 X-Large $10.00 $22.50 You can multiply by 0.1 and subtract from the original numbers. 6.75 13.50 7.20 15.75 8.10 18.00 9.00 20.25 7.5 15 8 17.5 9 20 10 22.5 7.5 15 8 17.5 9 20 10 22.5 7.5 15 8 17.5 9 20 10 22.5 0.75 1.5 0.8 1.75 0.9 2 1 2.25 – – 0.1 =

Homework: Page 251 #’s 18-22, 24-27, 29