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: 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: 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: 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: Yes, the sum of the elements of the third column would be the total enrollment of all three schools.

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 Scoreof Difficulty

A. Find the average of the elements in column 1, and interpret the results.

A. The average number of dives is 8.36.

B. The average score for the 6 dives is 8.36.

C. The average execution for the 6 dives is 8.36.

D. The average degree of difficulty for the 6 dives is 8.36.

_

_

_

_

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

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. Yes, adding the elements gives the total score.

B. No, the last element of the row is the product of the first and second elements in the row.

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 score for all 6 dives in the competition.

B. No, each score has a different degree of difficulty, so you can’t find the average.

Add and Subtract Matrices

Substitution

Add corresponding elements.

Simplify.

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.

Multiply a Matrix by a Scalar

Substitution

Multiply a Matrix by a Scalar

Multiply each element by 2.

Answer:

Simplify.

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

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.

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

• Homework

• Section 5 (pg 175):

• 13 – 31 odd, 28 (11 problems)

• 37 – 40 all (4 problems)