Post on 18-Jan-2016
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
You organized data into matrices.
• Analyze data in matrices.
• Perform algebraic operations with matrices.
• scalar
• scalar multiplication
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
T R/B E
Analyze Data with Matrices
Answer:
Analyze Data with Matrices
Answer: The average tuition cost for the three universities is $5935.
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
T R/B E
Analyze Data with Matrices
ISU = 6160 + 5958 = $12,118
UI = 6293 + 7250 = $13,543
UNI = 5352 + 6280 = $11,632
Answer:
Analyze Data with Matrices
ISU = 6160 + 5958 = $12,118
UI = 6293 + 7250 = $13,543
UNI = 5352 + 6280 = $11,632
Answer: University of Northern Iowa
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
T R/B E
Answer:
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
T R/B E
Answer: No, the first two elements of a row are in dollars and the third is in numbers of people.
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
T R/B E
Answer:
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
T R/B E
Answer: Yes, the sum of the elements of the third column would be the total enrollment of all three schools.
Add and Subtract Matrices
Substitution
Add corresponding elements.
Simplify.
Answer:
Add and Subtract Matrices
Substitution
Add corresponding elements.
Simplify.
Answer:
Add and Subtract Matrices
Answer:
–
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.
–
A.
B.
C.
D.
A.
B.
C.
D.
A.
B.
C.
D.
A.
B.
C.
D.
Multiply a Matrix by a Scalar
Substitution
Multiply a Matrix by a Scalar
Multiply each element by 2.
Answer:
Simplify.
Multiply a Matrix by a Scalar
Multiply each element by 2.
Answer:
Simplify.
A. B.
C. D.
A. B.
C. D.
Multi-Step Operations
Perform the scalar multiplication first. Then subtract the matrices.
Substitution
Distribute the scalars in each matrix.
4A – 3B
Multiply.
Subtract corresponding elements.
Answer:
Simplify.
Multi-Step Operations
Multiply.
Subtract corresponding elements.
Answer:
Simplify.
Multi-Step Operations
A.
B.
C.
D.
A.
B.
C.
D.
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
Short Long
Nails
Screws
CABINET
Short
Long
Nails
Screws
The company has orders for 3 desks and 4 cabinets. Express the company’s total needs for hardware in a single matrix.
Use Multi-Step Operations with Matrices
Write matrices.
Multiply scalars.
Add matrices.
Answer:
Use Multi-Step Operations with Matrices
Write matrices.
Multiply scalars.
Add matrices.
Short Long
Nails
Screws
Answer:
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
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