Matrix Practice Problems: Matrix Word Problems

Category : Matrix Practice Problems | Sub Category : Matrix Word Problems Posted on 2025-02-02 21:24:53

Matrix Practice Problems: Matrix Word Problems

Matrices are a fundamental concept in the field of mathematics and have a wide range of applications in various fields such as physics, computer science, and economics. Understanding how to work with matrices is essential for tackling complex problems and real-world scenarios. In this blog post, we will explore some matrix word problems to help you sharpen your skills in matrix operations and applications.

Problem 1:
A company manufactures two types of electronic products: laptops and tablets. The production matrix for a month is given by:
[ egin{bmatrix} 100 & 150 \ 80 & 120 end{bmatrix} ]
Each laptop sells for $800, and each tablet sells for $600. Calculate the total revenue from selling these products in a month.

Solution:
To calculate the total revenue, we need to multiply the production matrix by the price matrix:
[ egin{bmatrix} 100 & 150 \ 80 & 120 end{bmatrix} egin{bmatrix} 800 \ 600 end{bmatrix} = egin{bmatrix} 100*800 + 150*600 \ 80*800 + 120*600 end{bmatrix} = egin{bmatrix} 190000 \ 152000 end{bmatrix} ]
Therefore, the total revenue from selling laptops and tablets in a month is $190,000 + $152,000 = $342,000.

Problem 2:
A farmer has two types of fields: wheat and corn. The yield of each field per acre is given by the matrix:
[ egin{bmatrix} 4 & 3 \ 6 & 5 end{bmatrix} ]
If the farmer has 10 acres of wheat and 8 acres of corn, calculate the total yield of wheat and corn.

Solution:
To calculate the total yield, we need to multiply the yield matrix by the acres matrix:
[ egin{bmatrix} 4 & 3 \ 6 & 5 end{bmatrix} egin{bmatrix} 10 \ 8 end{bmatrix} = egin{bmatrix} 4*10 + 3*8 \ 6*10 + 5*8 end{bmatrix} = egin{bmatrix} 64 \ 70 end{bmatrix} ]
Therefore, the total yield of wheat is 64 units, and the total yield of corn is 70 units.

Matrix word problems provide a practical way to apply matrix operations in real-life situations. By practicing these problems, you can enhance your problem-solving skills and gain a deeper understanding of how matrices can be used to analyze and solve complex problems. Remember to break down the problems into manageable steps and utilize matrix multiplication and addition to arrive at the correct solutions.