Real-Life Matrix Applications and Transformations Quiz

A school is organizing a field trip for 120 students. If each bus can hold 30 students, how many buses are needed? Represent this situation using a matrix and solve for the number of buses.

• 6

• 4

• 5

• 3

A company produces two products, A and B. The profit from product A is $5 per unit, and from product B is $8 per unit. If they produce 50 units of A and 30 units of B, represent the profit using a matrix and calculate the total profit.

• 450

• 490

• 480

• 500

A video game uses a transformation matrix to rotate characters. If a character is at point (2, 3) and the rotation matrix is [[0, -1], [1, 0]], what are the new coordinates of the character after the transformation?

• (-3, 2)

• (-2, -3)

• (3, -2)

• (2, 3)

In a classroom, the number of boys and girls is represented by the matrix [[15], [10]]. If the school adds 5 more boys and 3 more girls, update the matrix to reflect the new numbers.

• [[18], [12]]

• [[22], [15]]

• [[20], [13]]

• [[15], [10]]

A restaurant has a menu with three items. The sales for each item over a week are represented by the matrix [[20, 30, 25], [15, 10, 5]]. Calculate the total sales for each item by summing the columns of the matrix.

• [40, 35, 25]

• [35, 40, 30]

• [30, 25, 20]

• [25, 30, 35]

A graphic designer uses a scaling matrix to enlarge an image. If the original dimensions of the image are represented by the matrix [[4], [6]], and the scaling factor is 2, what are the new dimensions of the image?

• [[2], [3]]

• [[8], [12]]

• [[6], [8]]

• [[4], [10]]

A sports team tracks their scores over five games using the matrix [[10, 20, 15, 25, 30]]. Calculate the average score per game by finding the mean of the matrix elements.

• 20

• 15

• 25

• 35

A factory produces two types of widgets. The production matrix is [[100, 150], [200, 250]]. If the factory increases production by 10% for each type, what will the new production matrix look like?

• [[100, 150], [200, 250]]

• [[120, 180], [240, 300]]

• [[110, 165], [220, 275]]

• [[90, 135], [180, 225]]

A city plans to build two parks. The area of the first park is represented by the matrix [[500]], and the second park by [[300]]. If they decide to combine the areas, what will the resulting area matrix be?

• [[700]]

• [[800]]

• [[600]]

• [[900]]

A photographer uses a transformation matrix to adjust the brightness of an image. If the original brightness levels are represented by the matrix [[50], [75], [100]], and the transformation matrix is [[1.2]], what are the new brightness levels?

• [[60], [90], [120]]

• [[1.2], [1.2], [1.2]]

• [[50], [75], [100]]

• [[70], [105], [140]]