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Five-Minute Check (over Chapter 3) Then/Now New Vocabulary Example 1: Dimensions and Elements of a Matrix Example 2: Real-World Example: Organize Data into a Matrix Example 3: Analyze Data with Matrices Lesson Menu

Solve each system of equations by using algebraic methods Solve each system of equations by using algebraic methods. 4x + 3y = 5 2y – x = 7 A. (–1, 3) B. (0, –7) C. (4, 1) D. (5, –5) A B C D 5-Minute Check 1

Solve each system of equations by using algebraic methods Solve each system of equations by using algebraic methods. y = 3x + 6 2x + 2y = –4 A. (–1, –1) B. (–2, 0) C. (1, 9) D. (2, 12) A B C D 5-Minute Check 2

A B C D Solve the system of inequalities by graphing. A. B. C. D. 5-Minute Check 3

The sum of two numbers is 2 The sum of two numbers is 2. The first number is 14 less than the second number. What are the numbers? A. –8, 6 B. –6, 8 C. 4, 10 D. 8, –10 A B C D 5-Minute Check 4

Bank A charges $0.10 per check and a $13 monthly fee for a checking account. Bank B charges $0.50 per check and a $5 monthly fee for a checking account. Darlene usually writes 15 checks per month. Which bank should she choose? How much will it cost her per month? A B C D A. Bank A, $14.50 B. Bank A, $12.50 C. Bank B, $14.50 D. Bank B, $12.50 5-Minute Check 5

You solved problems by organizing data in tables. Organize data in matrices. Use matrix row and column operations to analyze data. Then/Now

matrix equal matrices element dimensions row matrix column matrix square matrix zero matrix Vocabulary

A. State the dimensions of matrix G if Dimensions and Elements of a Matrix A. State the dimensions of matrix G if 2 rows 4 columns Answer: Since matrix G has 2 rows and 4 columns, the dimensions of matrix G are 2 × 4. Example 1

Dimensions and Elements of a Matrix B. Find the value of a12. Answer: Since a12 is the element in row 1, column 2, the value of a12 is –1. Example 1

A B C D A. State the dimensions of matrix G if G = A. 2 × 3 B. 2 × 2 Example 1

B. Find the value of a12. A. –1 B. 0 C. 2 D. 3 A B C D Example 1

University of Iowa: T - $6293 R/B - $7250 E - 30,409 Organize Data into a Matrix A. COLLEGE Kaitlin wants to attend one of three Iowa universities next year. She has gathered information about tuition (T), room and board (R/B), and enrollment (E) for the universities. Iowa State University: T - $6160 R/B - $5958 E - 26,160 University of Iowa: T - $6293 R/B - $7250 E - 30,409 University of Northern Iowa: T - $5352 R/B - $6280 E - 12,609 Organize the data in a matrix, with columns in order of tuition, room and board, and enrollment. Example 2

Organize the data into labeled columns and rows. Organize Data into a Matrix Organize the data into labeled columns and rows. T R/B E Answer: ISU UI UNI Example 2

University of Iowa: T - $6293 R/B - $7250 E - 30,409 Organize Data into a Matrix B. COLLEGE Kaitlin wants to attend one of three Iowa universities next year. She has gathered information about tuition (T), room and board (R/B), and enrollment (E) for the universities. Iowa State University: T - $6160 R/B - $5958 E - 26,160 University of Iowa: T - $6293 R/B - $7250 E - 30,409 University of Northern Iowa: T - $5352 R/B - $6280 E - 12,609 What are the dimensions of the matrix? What is the value of a32? Example 2

Organize Data into a Matrix T R/B E ISU UI UNI Answer: There are 3 rows and 3 columns, so the dimensions are 3 × 3. The value of a32, which is in the third row and second column, is 6280. Example 2

A. DINING OUT Justin is going out for lunch A. DINING OUT Justin is going out for lunch. The information he has gathered from two fast-food restaurants is listed below. Use a matrix to organize the information. A. B. C. D. Hamburger Cheeseburger Chicken Burger Complex Lunch Express Lunch Express Ham- burger Cheese- burger A B C D Example 2

B. DINING OUT Justin is going out for lunch B. DINING OUT Justin is going out for lunch. The information he has gathered from two fast-food restaurants is listed below. What are the dimensions of the matrix? What is the value of a31? A. 1 x 3; 3.39 B. 3 x 1; 3.59 C. 3 x 3; 4.99 D. 3 x x; 4.89 A B C D Example 2

Analyze Data with Matrices A. Use the matrix below that includes information on tuition (T), room and board (R/B), and enrollment (E) for three universities. ISU UI UNI T R/B E Find the average of the elements in column 1, and interpret the result. Example 3

Answer: The average tuition cost for the three universities is $5935. Analyze Data with Matrices Answer: The average tuition cost for the three universities is $5935. Example 3

Which University’s total cost is the lowest? Analyze Data with Matrices B. Use the matrix below that includes information on tuition (T), room and board (R/B), and enrollment (E) for three universities. ISU UI UNI T R/B E Which University’s total cost is the lowest? Example 3

Answer: University of Northern Iowa Analyze Data with Matrices ISU = 6160 + 5958 + = $12,118 UI = 6293 + 7250 = $13,543 UNI = 5352 + 6280 = $11,632 Answer: University of Northern Iowa Example 3

Analyze Data with Matrices C. Use the matrix below that includes information on tuition (T), room and board (R/B), and enrollment (E) for three universities. ISU UI UNI T R/B E Would adding the elements of the rows provide meaningful data? Explain. Answer: No, the first two elements of a row are in dollars and the third is in numbers of people. Example 3

Analyze Data with Matrices D. Use the matrix below that includes information on tuition (T), room and board (R/B), and enrollment (E) for three universities. ISU UI UNI T R/B E Would adding the elements of the third column provide meaningful data? Explain. Answer: Yes, the sum of the elements of the third column would be the total enrollment of all three schools. Example 3

Execution Degree Score of Difficulty The matrix displays Karen’s diving scores for her 6 dives at a competition. The total score is found by multiplying the degree of difficulty by the execution score. Dive 1 Dive 2 Dive 3 Dive 4 Dive 5 Dive 6 Execution Degree Score of Difficulty Example 3

A. Find the average of the elements in column 1, and interpret the results. A. The average number of dives is 8.3. B. The average score for the 6 dives is 8.3. C. The average execution for the 6 dives is 8.3. D. The average degree of difficulty for the 6 dives is 8.3. _ A B C D Example 3

B. The matrix displays Karen’s diving scores for her 6 dives at a competition. The total score is found by multiplying the degree of difficulty by the execution score. Which dive’s total is the highest? A. dive 1 B. dive 3 C. dive 4 D. dive 6 A B C D Example 3

C. The matrix displays Karen’s diving scores for her 6 dives at a competition. The total score is found by multiplying the degree of difficulty by the execution score. Would adding the elements of the rows provide meaningful data? Explain. A B A. Yes, adding the elements gives the total score. B. No, the last element of the row is the product of the second and third elements in the row. Example 3

D. The matrix displays Karen’s diving scores for her 6 dives at a competition. The total score is found by multiplying the degree of difficulty by the execution score. Would finding the average of the last column provide meaningful data? A. Yes, the average of the last column would be the average for all 6 dives in the competition. B. No, each score has a different degree of difficulty, so you can’t take the average. A B Example 3

End of the Lesson