Case Study Questions on Matrices for Class 12

Case Study Questions on Matrices for Class 12

Matrices Free Online Test | Class 12 Math Case Study Questions Practice

The Case Study Questions on Matrices Class 12 Mathematics helps students strengthen conceptual understanding and real-world application. Matrices play a critical role in solving linear equations and representing data in science and computer applications.

Our free online test is designed to simulate actual exam patterns. It features carefully selected math case study questions based on the CBSE Class 12 syllabus. These questions challenge students to apply concepts like identity matrices, invertibility, and matrix multiplication.

Because these tests are structured with reasoning and accuracy in mind, they support effective preparation. In fact, class 12 math case study questions in our test follow the same blueprint used in board exams.

Moreover, each question includes a one-line explanation. Therefore, students can immediately understand the logic behind the correct option.

Whether you’re looking to revise or practice, these math Case Study Questions on Matrices for class 12 offer great value. Also, scoring is automatic and instant. That motivates students to improve steadily.

In conclusion, mastering class 12 math case study questions through this online quiz will boost confidence. Try it now to stay ahead!

Case Study 3

Rohan is designing a robotic arm that must move in various directions based on coordinate instructions. To handle these instructions, he uses matrices to represent and process movement data. He performs addition, scalar multiplication, and matrix multiplication to determine the final position of the arm. During testing, he encounters situations where non-commutative multiplication leads to incorrect results if not carefully handled. To ensure safety and precision in his design, Rohan practices advanced operations on matrices and verifies results using matrix properties.

MCQ Questions:

1. What is the result of scalar multiplication \( 3 \times \begin{bmatrix} 2 & -1 \\ 0 & 4 \end{bmatrix} \)?

Answer: (a)
Solution: Scalar multiplication means multiplying each element by 3: \(3 \times 2 = 6\), \(3 \times -1 = -3\), etc.

2. What is the sum of matrices \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \) and \( B = \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix} \)?

Answer: (a)
Solution: Add corresponding elements: \(1+5=6\), \(2+6=8\), \(3+7=10\), \(4+8=12\).

3. Which operation is NOT always valid for any two matrices?

Answer: (d)
Solution: Multiplication of matrices is not always valid unless the number of columns in the first matrix equals the number of rows in the second.

4. The product of \( A = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \) and \( B = \begin{bmatrix} 5 & 7 \\ 2 & 3 \end{bmatrix} \) is:

Answer: (b)
Solution: Multiplying by the identity matrix leaves the matrix unchanged.

5. If \( A = \begin{bmatrix} 1 & 2 \end{bmatrix} \) and \( B = \begin{bmatrix} 3 \\ 4 \end{bmatrix} \), then the product \( AB \) is:

Answer: (b)
Solution: \( AB = 1 \times 3 + 2 \times 4 = 3 + 8 = 11 \), resulting in a \(1 \times 1\) matrix.