Matrices revision part 2

Multiple Select

Which of the matrices shown are permutation matrices?

• A

• B

• C

• D

• E

Multiple Choice

Which word is created when you pre multiply S by P?

• emit

• time

• mite

• item

• you can't premultiply S by P

Multiple Choice

Which word is created when you pre multiply R by P?

• evil

• veil

• veli

• live

• you can't premultiply R by P

Multiple Choice

Use the permutation matrix, Q, to rearrange the letters in R and S. What words are created?

• evil time

• veil time

• evil mite

• Q is not a permutation matrix

• veil mite

Multiple Choice

Which Matrix shows this information

Multiple Choice

How many ways are there to get to F?

• 1

• 2

• 3

• 4

Multiple Choice

Which Matrix shows the 2-step pathway from this information

Multiple Choice

In a round-robin chess tournament, there are 4 competitors: Bobby, Mikhail, Rajit and Vladimir.

Bobby beat Mikhail and Rajit.

Mikhail beat Rajit.

Vladimir lost to Rajit but beat Bobby and Mikhail.

Find the dominance matrix that represents this chess tournament.

Multiple Choice

The dominance matrix shows the results of a tennis tournament between Ben, Gina, Rex and Yasmin. Who did Gina defeat?

• Rex and Ben

• Ben and Yasmin

• Rex only

• Ben only

Multiple Choice

By finding the 2 step dominance matrix $$D^2$$ find the most dominant player by finding $$D+D^2$$

• Yasmin

• Ben and Yasmin

• Rex

• Ben only

Multiple Choice

The dominance matrix shows the results of a netball tournament. Which statement is NOT true?

• Red defeated Blue and Green

• Blue defeated Green and Yellow

• Green defeated Yellow

• Yellow defeated Green

Multiple Choice

A second-order dominance matrix X^2 is depicted above. Which of the following is true?

• Player A beat two players who beat B

• Player D beat B

• Player E lost to A

• Player C beat one player who beat E

Multiple Choice

$$S_5$$  is closest to:

Multiple Choice

$$S_1=$$  

Multiple Choice

The steady-state matrix is closest to:

Multiple Choice

What percentage of road that needs no maintenance will again need no maintenance the following year?

• 50%

• 5%

• 10%

• 20%

Multiple Choice

How many kilometres of highway need to be graded (G) in 2018?

• 700

• 400

• 200

• 1400

Multiple Choice

How many kilometres of highway will need to be resurfaced in 2019?

• 460

• 390

• 360

• 1490

Multiple Choice

A population of birds migrates each year to a remote island with four nesting sites: A, B, C and D. The transition matrix can be used to predict the number of birds nesting at each of the four sites in subsequent years. Two thousand eight hundred birds nest at site C in 2008. Of these, the number that nest at site A in 2009 is predicted to be:

• 560

• 980

• 1680

• 2800

• 3360

Multiple Choice

This transition matrix predicts that, in the long term, the mutton birds will:

• nest only at site A

• nest only at site B

• nest only at sites A and C

• nest only at sites B and D

• continue to nest at all four sites

Multiple Choice

Six thousand birds nest at site B in 2008. Assume that an equal number of mutton birds nested at each of the four sites in 2007. The same transition matrix applies. The total number of birds that nested on the island in 2007 was:

• 6000

• 8000

• 12000

• 16000

• 24000

Fill in the Blanks

Multiple Choice

Construct a Leslie Matrix.

Multiple Choice

The initial population of mammals is 22: 0-4 month and 4-8 month olds, 18: 8-12 month olds, 20: 12-16 month olds, 7: 16-20 month olds and 2: 20-24 month olds. Construct a matrix for the initial population.

• P = [22 18 20 7 2]

• P= [22 22 18 7 2]

• P= [22 22 18 20 7 2]

• P= [22 18 20 7 2 0]

Multiple Choice

How many 12-16 month olds are there in 20 months?

• 61.85

• 80.74

• 247.83

• 20.28

Multiple Choice

What is the total population after 16 months? round to the whole mammal.

• 55

• 143

• 170

• 449

Multiple Choice

What is the long term growth rate of this herd?

• 4.8%

• 8.1%

• 9.9%

• 12.1%