Lesson Menu Five-Minute Check (over Lesson 3–4) Then/Now New Vocabulary Example 1: Real-World Example: Analyze Data with Matrices Key Concept: Adding and Subtracting Matrices Example 2: Add and Subtract Matrices Key Concept: Multiplying by a Scalar Example 3: Multiply a Matrix by a Scalar Key Concept: Properties of Matrix Operations Example 4: Multi-Step Operations Example 5: Real-World Example: Use Multi-Step Operations with Matrices

Then/Now You organized data into matrices. Analyze data in matrices. Perform algebraic operations with matrices.

Vocabulary scalar scalar multiplication

Example 1 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. Find the average of the elements in column 1, and interpret the result. ISU UI UNI TR/BE

Example 1 Analyze Data with Matrices Answer:

Example 1 Analyze Data with Matrices Answer: The average tuition cost for the three universities is $5935.

Example 1 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. Which university’s total cost is the lowest? ISU UI UNI TR/BE

Example 1 Analyze Data with Matrices ISU = = $12,118 UI = = $13,543 UNI = = $11,632 Answer:

Example 1 Analyze Data with Matrices ISU = = $12,118 UI = = $13,543 UNI = = $11,632 Answer: University of Northern Iowa

Example 1 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. Would adding the elements of the rows provide meaningful data? Explain. ISU UI UNI TR/BE Answer:

Example 1 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. Would adding the elements of the rows provide meaningful data? Explain. ISU UI UNI TR/BE Answer: No, the first two elements of a row are in dollars and the third is in numbers of people.

Example 1 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. Would adding the elements of the third column provide meaningful data? Explain. ISU UI UNI TR/BE Answer:

Example 1 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. Would adding the elements of the third column provide meaningful data? Explain. ISU UI UNI TR/BE Answer: Yes, the sum of the elements of the third column would be the total enrollment of all three schools.

Concept

Example 2 Add and Subtract Matrices Substitution Add corresponding elements. Simplify. Answer:

Example 2 Add and Subtract Matrices Substitution Add corresponding elements. Simplify. Answer:

Example 2 Add and Subtract Matrices Answer: –

Example 2 Add and Subtract Matrices Answer: Since the dimensions of A are 2 × 3 and the dimensions of B are 2 × 2, these matrices cannot be subtracted. –

Example 2 A. B. C. D.

Example 2 A. B. C. D.

Example 2 A. B. C. D.

Example 2 A. B. C. D.

Concept

Example 3 Multiply a Matrix by a Scalar Substitution

Example 3 Multiply a Matrix by a Scalar Multiply each element by 2. Answer: Simplify.

Example 3 Multiply a Matrix by a Scalar Multiply each element by 2. Answer: Simplify.

Example 3 A.B. C.D.

Example 3 A.B. C.D.

Concept

Example 4 Multi-Step Operations Perform the scalar multiplication first. Then subtract the matrices. Substitution Distribute the scalars in each matrix. 4A – 3B

Example 4 Multiply. Subtract corresponding elements. Answer: Simplify. Multi-Step Operations

Example 4 Multiply. Subtract corresponding elements. Answer: Simplify. Multi-Step Operations

Example 4 A. B. C. D.

Example 4 A. B. C. D.

Example 5 Use Multi-Step Operations with Matrices BUSINESS A small company makes unfinished desks and cabinets. Each item requires different amounts of hardware as shown in the matrices. DESK ShortLong Nails Screws CABINET ShortLong Nails Screws The company has orders for 3 desks and 4 cabinets. Express the company’s total needs for hardware in a single matrix.

Example 5 Use Multi-Step Operations with Matrices Write matrices. Multiply scalars. Add matrices. Answer:

Example 5 Use Multi-Step Operations with Matrices Write matrices. Multiply scalars. Add matrices. ShortLong Nails Screws Answer:

Example 5 Miniature golf course A has 50 blue golf balls, 100 yellow golf balls, and 50 green golf balls. Miniature golf course B has 150 blue golf balls, 100 yellow golf balls, and 25 green golf balls. Miniature golf course C has 40 blue golf balls, 70 yellow golf balls, and 80 green golf balls. Express the total number of each color golf ball in a single matrix. Blue Yellow Green A.B. C.D. Blue Yellow Green Course A Course B Course C Course A Course B Course C

Example 5 Miniature golf course A has 50 blue golf balls, 100 yellow golf balls, and 50 green golf balls. Miniature golf course B has 150 blue golf balls, 100 yellow golf balls, and 25 green golf balls. Miniature golf course C has 40 blue golf balls, 70 yellow golf balls, and 80 green golf balls. Express the total number of each color golf ball in a single matrix. Blue Yellow Green A.B. C.D. Blue Yellow Green Course A Course B Course C Course A Course B Course C