Matrix Transformations and Real-World Applications for 8th Graders

A company produces two types of gadgets, A and B. The production matrix is given as \( P = \begin{bmatrix} 3 & 2 \\ 1 & 4 \end{bmatrix} \). If they produce 10 units of A and 5 units of B, how many total gadgets are produced?

• 50

• 60

• 70

• 80

A school has a matrix representing the number of students in different grades: \( S = \begin{bmatrix} 30 & 25 \\ 20 & 15 \end{bmatrix} \). If the school adds 5 students to each grade, what will the new matrix look like?

• [[30, 30], [25, 25]]

• [[35, 25], [20, 15]]

• [[35, 30], [25, 20]]

• [[30, 25], [20, 15]]

A delivery service uses a matrix to track deliveries: \( D = \begin{bmatrix} 2 & 3 \\ 4 & 1 \end{bmatrix} \). If they double the number of deliveries, what is the new delivery matrix?

• [[2, 6], [4, 2]]

• [[4, 6], [8, 2]]

• [[4, 3], [8, 1]]

• [[0, 0], [0, 0]]

Two friends, Alex and Jamie, are selling lemonade and cookies. The profit matrix is \( P = \begin{bmatrix} 5 & 3 \\ 2 & 4 \end{bmatrix} \). If they sell 10 lemonades and 15 cookies, what is their total profit?

• 70

• 100

• 95

• 80

A farmer has a matrix representing the area of land used for crops: \( A = \begin{bmatrix} 10 & 5 \\ 8 & 12 \end{bmatrix} \). If he increases the area of each crop by 2 acres, what will the new area matrix be?

• [[12, 5], [8, 12]]

• [[12, 7], [10, 14]]

• [[10, 5], [8, 12]]

• [[14, 9], [10, 16]]

In a video game, a character can move in a grid represented by a matrix: \( M = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \). If the character moves right and up, what is the new position matrix?

• [[1, 0]]

• [[0, 1]]

• [[0, 0]]

• [[1, 1]]

A store sells two products, X and Y. The sales matrix is \( S = \begin{bmatrix} 20 & 30 \\ 15 & 25 \end{bmatrix} \). If the store has a sale and reduces the price of X by 5 and Y by 10, what is the new sales matrix?

• [[20, 30], [20, 30]]

• [[25, 30], [15, 35]]

• [[30, 40], [10, 20]]

• [[25, 40], [15, 25]]

A restaurant has a matrix for the number of meals served each day: \( R = \begin{bmatrix} 50 & 40 \\ 30 & 20 \end{bmatrix} \). If they serve 10 more meals each day, what will the updated matrix be?

• [[60, 40], [30, 20]]

• [[70, 60], [50, 40]]

• [[50, 40], [30, 20]]

• [[60, 50], [40, 30]]

A gym tracks the number of members in different classes using a matrix: \( G = \begin{bmatrix} 15 & 25 \\ 10 & 20 \end{bmatrix} \). If they gain 5 new members in each class, what is the new member matrix?

• [[15, 25], [10, 20]]

• [[25, 35], [20, 30]]

• [[20, 25], [15, 20]]

• [[20, 30], [15, 25]]

A factory produces two products, P1 and P2, represented by the matrix \( F = \begin{bmatrix} 100 & 150 \\ 200 & 250 \end{bmatrix} \). If the factory increases production by 10% for each product, what will the new production matrix be?

• [[120, 180], [240, 300]]

• [[105, 157.5], [210, 262.5]]

• [[100, 150], [200, 250]]

• [[110, 165], [220, 275]]