Real-Life Matrix Applications: Determinants & Inverses

A store sells 3 types of fruits: apples, bananas, and oranges. The sales for each fruit over three days are represented by the matrix A = [[10, 15, 20], [12, 18, 25], [14, 22, 30]]. Calculate the determinant of matrix A to determine if the sales data is consistent.

• 0

• -10

• 15

• -5

A company has three departments: Sales, Marketing, and Production. The number of employees in each department is represented by the matrix B = [[50], [30], [20]]. If the company wants to double the number of employees in each department, what will the new matrix look like?

• [[100], [60], [40]]

• [[120], [70], [50]]

• [[80], [60], [40]]

• [[100], [50], [30]]

A school has 4 classes with the following number of students: Class 1 has 25 students, Class 2 has 30 students, Class 3 has 20 students, and Class 4 has 15 students. Represent this data in a matrix C and find the inverse of matrix C if possible.

• Inverse of matrix C is not possible.

• Inverse of matrix C is possible and equals [[0.04, -0.04, 0.06, 0.08], [-0.02, 0.03, -0.01, 0.01], [0.01, -0.02, 0.05, -0.03], [0.02, 0.01, -0.02, 0.04]]

• Inverse of matrix C is 1.

• Inverse of matrix C is a 4x4 identity matrix.

A restaurant's weekly sales are represented by the matrix D = [[2000, 1500], [1800, 2200]]. If the restaurant wants to find the average sales for each week, how can they use matrix operations to achieve this?

• The average sales for each week are [2000, 1500].

• The average sales for each week are [1900, 1850].

• The average sales for each week are [1850, 1900].

• The average sales for each week are [2100, 1800].

A delivery service has three routes with the following costs: Route 1 costs $50, Route 2 costs $70, and Route 3 costs $90. Represent these costs in a matrix E and find the total cost if they deliver to all three routes once.

• $150

• 210

• $180

• $200

A video game company tracks the number of games sold in three regions: North, South, and East. The sales data is represented by the matrix F = [[100], [150], [200]]. If the company wants to find the total sales, how can they use matrix addition?

• 450

• 4500

• 600

• 300

A car rental service has a matrix G representing the number of cars rented each day for a week: [[5, 7, 6], [8, 9, 10], [4, 5, 6]]. Calculate the total number of cars rented over the week using matrix operations.

• 55

• 60

• 65

• 70

A factory produces three products with the following profit margins: Product A: $20, Product B: $30, Product C: $40. Represent this data in a matrix H and calculate the total profit if they sell 10 of each product.

• $1000

• $800

• 900

• $750

A sports team tracks their scores over five games represented by the matrix I = [[80, 90, 85, 95, 100]]. If they want to find the average score, how can they use matrix operations to calculate this?

• 85

• 100

• 95

• 90

A transportation company has a matrix J representing the number of packages delivered each day for a week: [[15, 20, 25], [30, 35, 40]]. If they want to find the total number of packages delivered, how can they use matrix addition?

• 200

• 165

• 150

• 180