Matrices Workshop

(they're everywhere if you where to look)

people,round and lattice by flickr user jmsmytaste

To reduce traffic congestion a city planner proposed the conversion of some downtown streets to one-way streets. The new plan is below.

(a) Construct a network matrix to represent the new plan.

(b)Determine the number of ways a tourist could get from the Art Gallery to the Tourist Centre and see exactly 3 sites along the way.

Library Museum City Hall Water Park

Tourist CentreCourt HouseArt Gallery

HOMEWORK

Solve for x and y. HOMEWORK

Solve for x and y.

Wickers Furniture has two retail stores, A and B. Their inventory for the number of sofas, recliners, dressers, and dinettes is given in the table below.

(d) Write a 4 x 4 square matrix where the elements of the main diagonal are the prices, and all other elements are zeros. Label this matrix D. Find AD. What do the values in matrix AD represent?

(c) Calculate AB to determine the value of the inventory at each store. Label the new matrix C, and save it.

(b) Write a 4 x 1 column matrix that shows the prices, and name it B.(a) Write a 2 x 4 matrix for the inventory and name it A.

Sofas cost $800 each, recliners $525 each, dressers $650 each, and dinettes $750 each.

sofas recliners dressers dinettesStore A 7 12 10 19Store B 15 6 8 9

Wickers Furniture has two retail stores, A and B. Their inventory for the number of sofas, recliners, dressers, and dinettes is given in the table below.

(a) Write a 2 x 4 matrix for the inventory and name it A.

Sofas cost $800 each, recliners $525 each, dressers $650 each, and dinettes $750 each.

sofas recliners dressers dinettesStore A 7 12 10 19Store B 15 6 8 9

Wickers Furniture has two retail stores, A and B. Their inventory for the number of sofas, recliners, dressers, and dinettes is given in the table below.

(d) Write a 4 x 4 square matrix where the elements of the main diagonal are the prices, and all other elements are zeros. Label this matrix D. Find AD. What do the values in matrix AD represent?

(c) Calculate AB to determine the value of the inventory at each store. Label the new matrix C, and save it.

(b) Write a 4 x 1 column matrix that shows the prices, and name it B.

Sofas cost $800 each, recliners $525 each, dressers $650 each, and dinettes $750 each.

sofas recliners dressers dinettesStore A 7 12 10 19Store B 15 6 8 9

Wickers Furniture has two retail stores, A and B. Their inventory for the number of sofas, recliners, dressers, and dinettes is given in the table below.

(d) Write a 4 x 4 square matrix where the elements of the main diagonal are the prices, and all other elements are zeros. Label this matrix D. Find AD. What do the values in matrix AD represent?

(c) Calculate AB to determine the value of the inventory at each store. Label the new matrix C, and save it.

sofas recliners dressers dinettesStore A 7 12 10 19Store B 15 6 8 9

Wickers Furniture has two retail stores, A and B. Their inventory for the number of sofas, recliners, dressers, and dinettes is given in the table below.

(d) Write a 4 x 4 square matrix where the elements of the main diagonal are the prices, and all other elements are zeros. Label this matrix D. Find AD. What do the values in matrix AD represent?

sofas recliners dressers dinettesStore A 7 12 10 19Store B 15 6 8 9

I have two coins in a bag, a fair coin and a biased (double headed) coin. The fair coin is tossed first. If the result of the previous toss is a head, then the biased coin is tossed next. If the result of the previous toss is a tail, then the fair coin is tossed next. Use transition matrices to describe the sequence of likely outcomes. What happens if a different biased coin with both head and tail sides, but biased 60:40 in favour of tails is used instead?

HOMEWORK

A large grain cleaning plant has five centres of operation identified as A, B, C, D, and E. These sites are connected with conveyor belts to move grain as follows:

(c) Can grain be moved from any site to any other site using no more than two trips on the conveyor belt? If not, then indicate which sites cannot be connected in this way. Explain how you determine this answer.

(b) Write matrix B to represent the number of ways grain can be moved between sites via one other site.

(a) Create a square matrix A to represent the direct routes between sites. A '1' represents a direct route, and a '0' represents no direct route.

A can move grain to B and DB can move grain to A and CC can move grain to DD can move grain to EE can move grain to A and CHOMEWORK

A bowler bowls only medium pace and spin. When a medium pace ball has been bowled, the probability that the next ball is bowled using spin is 7/4. When a spin ball has been bowled, the probability that the next ball is bowled using medium pace is 2/3. For each of the possible first ball choices (medium pace or spin) find the probabilities associated with each of the following balls of the over being bowled as medium pace or spin. HOMEWORK

Solve for x: HOMEWORK

Write a square network matrix where each element represents the number of direct paths between points or towns. List the matrix entries in alphabetical order. HOMEWORK