Case Study Problems on Matrices and Determinants

Math Case Study Problems on Matrices and Determinants for Class 12

Free Online Test – Matrices and Determinants for Class 12

The Case Study on Matrices and Determinants Class 12 Mathematics focuses on strengthening your problem-solving skills with real exam-level questions. It is based on math case study questions specifically crafted for Class 12 CBSE students.

This free online test includes class 12 math case study questions from all subtopics, such as matrix multiplication, inverse of a matrix, and properties of determinants. Therefore, it serves as a great revision resource before board exams.

Moreover, the questions mirror the latest board exam patterns. You’ll find math case study questions for class 12 that challenge your application and analytical abilities.

In addition, students benefit from instant feedback, helping them identify and improve weak concepts. The tests are structured and easy to follow.

As a result, consistent practice with these questions enhances accuracy, speed, and overall performance in CBSE board exams.

Case Study 3

A small business owner, Rajiv, needed to manage his warehouse inventory based on supply and demand across three locations. He modeled his inventory flow using a system of three linear equations representing quantities shipped to and from locations. To find the exact values for each route, he expressed the system in matrix form and applied the inverse matrix method. Rajiv used the determinant of the coefficient matrix to check if a unique solution exists. Additionally, he applied cofactor and adjoint concepts to calculate the matrix inverse and solve for the unknowns. Let us explore how determinants help in such business optimization tasks.

1. If the determinant of a 3×3 matrix is zero, what does it imply about the system of equations it represents?

Answer: (b) – A zero determinant implies the matrix is singular, so the system has either infinitely many or no solution.

2. Given matrix A = [[1, 2, 3], [0, 4, 5], [1, 0, 6]], find det(A).

Answer: (a) – det(A) = 24 + 10 – 12 = 22

3. Which of the following statements about cofactors is true?

Answer: (c) – Cofactors are needed to compute both the determinant (via expansion) and the adjoint matrix.

4. What is the order of an identity matrix used to invert a 3×3 matrix?

Answer: (d) – The identity matrix must be of the same order as the matrix being inverted.

5. The inverse of a matrix A is found using which formula?

Answer: (c) – The correct formula is A-1 = 1/det(A) × adj(A) if det(A) ≠ 0.