This table shows the number of customers walking through the doors of two businesses over a long weekend:
Organise the data into a matrix. Let the position of each element be the same as the position in the table.
What is the size of the matrix?
| Saturday | Sunday | Monday | |
|---|---|---|---|
| Florist | 140 | 110 | 98 |
| Butcher | 150 | 118 | 135 |
This table displays the average temperature (in degrees Celsius) in two cities for each season:
| Summer | Autumn | Winter | Spring | |
|---|---|---|---|---|
| Perth | 30 | 25 | 17 | 28 |
| Melbourne | 32 | 26 | 15 | 27 |
This data is organised into the matrix:
Do the rows of the matrix represent the temperatures for each season or for each city?
What is the size of the matrix?
Identify the element in t_{23} and interpret its meaning in context
Mia has a part-time job. Each week, she earns money and saves some of it.
The matrix represents the amounts earned \left(E\right) and saved \left(S\right), in dollars, in each of three weeks.
How much did Mia save in Week 1?
Which week did Mia save the most money?
Determine how much Mia earned in total over the three weeks.
\begin{array}{cc} & \begin{array}{cc} E & S \end{array} \\ \begin{array}{c} \text{Week } 1 \\ \text{Week } 2 \\ \text{Week } 3 \end{array} & \left[ \begin{array}{cc} 500 & 250 \\ 480 & 200 \\ 450 & 230 \end{array}\right] \end{array}
The number of hours worked by Alex \left(A\right), Beth \left(B\right), Charlie \left(C\right), Dana \left(D\right), and Ethan \left(E\right) across five days of a week (Monday, Tuesday, Wednesday, Thursday, Friday) is shown in the matrix:
\begin{array}{cc} & \begin{array}{ccccc} \text{M} & \text{Tu} & \text{W} & \text{Th} & \text{F} \end{array} \\ \begin{array}{c} A \\ B \\ C \\ D \\ E \end{array} & \left[ \begin{array}{ccccc} 8 \, \, \, & 8\, \, \, & 8 \, \, \, & 6 \, \, \, & 5 \\ 7 \, \, \, & 8 \, \, \, & 9 \, \, \,& 8 \, \, \, & 7 \\ 6\, \, \, & 6\, \, \, & 6\, \, \, & 6\, \, \, & 6 \\ 9\, \, \, & 9\, \, \, & 7 \, \, \,& 8\, \, \, & 9 \\ 5\, \, \, & 6\, \, \, & 7\, \, \, & 8 \, \, \,& 9 \end{array}\right] \end{array}
How many hours did Charlie work on Wednesday?
Who worked 9 hours on Friday?
Calculate the total number of hours worked by Beth during the week.
Who worked the most hours on Monday?
Jack, a chef, is known for these two recipes:
Crazy Cookie which contains:
360 \operatorname{ g} of yeast
410 \operatorname{ g} of salt
340 \operatorname{ g} of flour
230 \operatorname{ g} of sugar
120 \operatorname{ g} of honey
Scrumptious Surprise which contains:
420 \operatorname{ g} of yeast
390 \operatorname{ g} of salt
330 \operatorname{ g} of flour
200 \operatorname{ g} of sugar
80 \operatorname{ g} of honey
Represent the amounts into a 2 \times 5 matrix.
A long jump competition was down to four competitors in the final. Uther jumped 7.4 \text{ m}, 5.7 \text{ m} and 7.5 \text{ m} in his attempts. Yuri jumped 6.7 \text{ m}, 7.3 \text{ m} and 6.9 \text{ m}. Vincent jumped 7.1 \text{ m}, 5.9 \text{ m} and 6.8 \text{ m}, and Luigi jumped 5.6 \text{ m}, 6.1 \text{ m} and 6.3 \text{ m}.
Represent the data into a 3 \times 4 matrix.
The friendships between five children are summarised in a graph.
Represent this information in a matrix, using a 0 to indicate no friendship and a 1 to indicate friendship.
The leading diagonal from top left to bottom right contains all zeros. Why is this?
The path connecting various buildings on a university campus are shown in the graph:
Represent the path connections in a matrix.
Represent the road connections, alphabetically, in this map using a matrix.
Consider this map:
Construct a matrix to represent the major roads (in yellow) connecting the towns, in alphabetical order.
The Riverdale Soccer Club has five new players join its team: Jamie, Kai, Lisa, Max and Noah.
The graph shows the players who have played soccer together before joining the team. For example, the edge between Jamie and Kai shows that they have previously played soccer together.
Represent this information in a matrix.
How many of these players had Max played soccer with before joining the team?
Who had played soccer with both Kai and Noah before joining the team?
During the season, another new player, Olivia, joined the team. Olivia had not played soccer with any of these players before. Add this information to the matrix.
The distances, in kilometres, along three major roads between the Californian cities San Francisco \left(S\right), Los Angeles \left(L\right), and San Diego \left(D\right), are displayed in the matrix:
\begin{array}{cc} & \begin{array}{ccc} S \quad & L\quad & D \end{array} \\ \begin{array}{c} S \\ L \\ D \end{array} & \left[ \begin{array}{ccc} 0 & 610 & 800 \\ 610 & 0 & 120 \\ 800 & 120 & 0 \end{array}\right] \end{array}
What is the distance, in kilometres, between San Francisco and Los Angeles?
Jamie drove 120\operatorname{km} directly between two of the Californian cities. Which two cities did she drive between?
The Martinez family would like to drive from San Francisco to Los Angeles, and then to San Diego. Determine the total distance in kilometres that they will travel.
A clothing store has three locations: Location X, Location Y, and Location Z. These locations sell three types of clothing: shirts \left(S\right), pants \left(P\right), and jackets \left(J\right). The table lists the number of each type of clothing in three different sizes that are currently held at each location.
| Location | Small | Medium | Large |
|---|---|---|---|
| \text{Location } X | 5 \text{ shirts} | 3 \text{ pants} | 2 \text{ jackets} |
| \text{Location } Y | 4 \text{ pants} | 6 \text{ shirts} | 3 \text{ jackets} |
| \text{Location } Z | 2 \text{ jackets} | 4 \text{ shirts} | 3 \text{ pants} |
Complete the matrix that shows the total number of each type of clothing (Shirts, Pants, Jackets) in each size across all locations.
\begin{array}{cc} & \begin{array}{ccc} S & P & J \end{array} \\ \begin{array}{c} \text{Small} \\ \text{Medium} \\ \text{Large} \end{array} & \left[ \begin{array}{ccc} & & & \\ & & & \\ & & & \end{array}\right] \end{array}
The elements in matrix M represent the costs (in dollars) for different materials required for two types of construction projects (Project A and Project B) at two different suppliers (Supplier X and Supplier Y). The cost details are shown:
Cost of Material 2 for Project A from Supplier X= 150
Cost of Material 1 for Project A from Supplier X=200
Cost of Material 1 for Project B from Supplier X = 180
Cost of Material 1 for Project B from Supplier Y= 220
Cost of Material 2 for Project B from Supplier Y= 210
Cost of Material 2 for Project A from Supplier Y= 170
Determine the size of matrix M.
Construct matrix M.
What type of matrix is M?
This map network shows the roads that connect three towns:
Create a 3 \times 3 matrix which represents the direct paths between the three towns. For the rows and columns, use the order of towns as: Arwick then Bogville then Caraway.
This network shows the roads that connect five towns:
Create a 5 \times 5 matrix which represents the direct paths between the towns. For the rows and columns, put the towns in alphabetical order.
Create a 5 \times 5 matrix which represents the paths between the towns using exactly two paths (or exactly one stop-over).
Consider the image which shows a train network and the stations that are connected by train lines:
Construct a matrix that represents the train network, in order from left to right.
List the stations that would be passed if travelling from the airport to PSU.
The matrix shown displays the number of roads connecting five towns: Arlington \left(A\right), Bristol \left(B\right), Camden \left(C\right), Dover \left(D\right) and Elmont \left(E\right).
N = \begin{bmatrix} 0 & 1 & 2 & 0 & 1 \\ 1 & 0 & 0 & 1 & 2 \\ 2 & 0 & 0 & 1 & 1 \\0 & 1 & 1 & 0 & 0 \\ 1 & 2 & 1 & 0 & 0 \end{bmatrix}
Construct a road map using the information shown.
Determine whether these statements are true or false.
There is a road loop at Bristol.
You can travel directly between Camden and Elmont.
There are two roads connecting Arlington and Camden.
There are three different ways to travel between Bristol and Elmont.
A major flood washes away part of the road connecting Arlington and Camden. Which elements in matrix N will need to be changed to reflect the new road conditions between the towns?
The matrix T shows the results of a round-robin chess tournament among six friends: Alan \left(A\right), Beth \left(B\right), Carlos \left(C\right), Dana \left(D\right), Evan \left(E\right) and Fiona \left(F\right). Each participant played against every other participant exactly once. A 1 in the matrix indicates that the player in that row defeated the player in the corresponding column, and a 0 indicates a loss.
T = \begin{array}{cc} & \begin{array}{cccccc} A & B & C & D & E & F \end{array} \\ \begin{array}{c} A \\ B \\ C \\ D \\ E \\ F \end{array} & \left[ \begin{array}{cccccc} 0 & 1 & 0 & 1 & 1 & 0 \\ 0 & 0 & 1 & 0 & 1 & 1 \\ 1 & 0 & 0 & 1 & 0 & 1 \\ 0 & 1 & 0 & 0 & 1 & 0 \\ 0 & 0 & 1 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 & 0 & 0 \end{array}\right] \end{array}
Identify the error in the matrix. Justify using mathematical reasoning.
A beach volleyball social competition team can have 3 players on the court at any time. The team has 5 players at the tournament. The table shows 3 combinations that the coach has already used in the first three games.
There is one more game left in the tournament. Who should the coach choose to play so that every team member has played with every other team member at least once?
Justify your answer using a matrix.
| Games | Players chosen |
|---|---|
| 1 | \text{Ryan, Jimmy, Lucy} |
| 2 | \text{Lucy, Beth, Ellie} |
| 3 | \text{Ellie, Ryan, Jimmy} |
Represent this food chain in a matrix.
Rabbits and squirrels both eat plants.
Foxes and hawks eat both rabbits and squirrels.
A few colleagues decided to carpool on the way to work. The matrix displays the distances between each house.
Determine the shortest route that starts at House A and visits every house exactly once.
\begin{array}{cc} & \begin{array}{ccccc} A & B & C & D & E \end{array} \\ \begin{array}{c} A \\ B \\ C \\ D \\ E \end{array} & \left[ \begin{array}{ccccc} 0 & 14 & 0 & 12 & 17 \\ 14 & 0 & 17 & 10 & 0 \\ 0 & 17 & 0 & 13 & 19 \\ 12 & 10 & 13 & 0 & 15 \\ 17 & 0 & 19 & 15 & 0 \end{array}\right] \end{array}