Boost Your Performance in CBSE Class 12 Mathematics Exam Chapter 3 with These Important Questions
FAQs on Important Questions for CBSE Class 12 Maths Chapter 3 - Matrices 2024-25
1. What is the expected marks weightage for the Matrices chapter in the CBSE Class 12 Maths board exam 2025-26?
In the CBSE Class 12 Maths board exam for 2025-26, the Matrices chapter is part of the 'Algebra' unit, which it shares with Determinants. The combined weightage for this unit is typically around 10 marks. You can expect questions from Matrices worth approximately 5-7 marks, ranging from MCQs to short and long-answer questions.
2. Which topics from Matrices are most important for 1-mark or MCQ questions in the 2025-26 board exam?
For 1-mark or Multiple Choice Questions (MCQs), the most frequently tested concepts from the Matrices chapter include:
- Determining the order of a matrix.
- Identifying types of matrices (e.g., square, diagonal, identity, zero matrix).
- Questions on the equality of matrices to find the value of variables.
- Calculating the number of possible matrices given the number of elements or entries.
- Basic matrix operations like addition and scalar multiplication.
3. What are some expected long-answer (3 or 5-mark) questions from Chapter 3, Matrices?
For the higher-marks sections, important question types from Matrices that are often asked in board exams include:
- Solving a matrix equation involving addition, subtraction, and multiplication to find an unknown matrix.
- Questions that require the application of properties of the transpose of a matrix, such as verifying (AB)' = B'A'.
- The most important long-answer question is to express a given square matrix as the sum of a symmetric and a skew-symmetric matrix.
4. What are the frequently repeated question types from the Matrices chapter in previous CBSE Class 12 board papers?
Based on board exam trends, some of the most frequently repeated questions from Matrices are:
- Constructing a matrix of a specific order (e.g., 2x2 or 3x2) where the elements are defined by a rule, like aᵢⱼ = i + 2j.
- Finding values of x, y, z from two equal matrices.
- Proving that for a square matrix A, the matrices (A + A') and (A - A') are symmetric and skew-symmetric, respectively.
- Word problems that can be represented and solved using matrix multiplication.
5. Why is matrix multiplication not commutative? Explain, as this concept is often tested in board exams.
Matrix multiplication is not commutative because the product AB is generally not equal to the product BA. This is a fundamental property tested to check conceptual clarity. The primary reason is the row-by-column multiplication rule. The element in the i-th row and j-th column of AB is the dot product of the i-th row of A and the j-th column of B. When the order is reversed to BA, the rows of B are multiplied by the columns of A, which yields a completely different result. For example, if A = [[1, 2], [3, 4]] and B = [[0, 1], [1, 0]], then AB = [[2, 1], [4, 3]] while BA = [[3, 4], [1, 2]]. Clearly, AB ≠ BA.
6. What is the most common mistake students make when dealing with important questions on matrix multiplication?
The most common mistake is assuming matrix multiplication is commutative (i.e., AB = BA), which is incorrect. Another frequent error occurs during the multiplication process itself: students might multiply corresponding elements instead of following the 'row-by-column' rule. To avoid this, always check the order of the matrices to ensure they are compatible for multiplication (columns of the first must equal rows of the second) and carefully multiply each row of the first matrix with each column of the second matrix.
7. How does the concept of a singular matrix relate to the invertibility of a matrix, and why is this an important concept for board exam questions?
A square matrix A is called singular if its determinant, |A|, is zero. It is non-singular if |A| ≠ 0. This concept is critical because a matrix is invertible (meaning its inverse A⁻¹ exists) if and only if it is non-singular. This forms a crucial link between the chapters on Matrices and Determinants. Questions often test this by asking you to find values of a variable 'k' that would make a matrix singular, thereby making it non-invertible.
8. What is the importance of the theorem used to express a square matrix as the sum of a symmetric and a skew-symmetric matrix?
This is one of the most important theorems for long-answer questions in board exams. Its importance lies in demonstrating that any square matrix can be uniquely decomposed into two special types of matrices. The formula used is A = ½(A + A') + ½(A - A'), where A is the given square matrix, A' is its transpose, ½(A + A') is a symmetric matrix, and ½(A - A') is a skew-symmetric matrix. This question is a test of multiple skills: finding the transpose, matrix addition/subtraction, scalar multiplication, and verifying the properties of the resulting matrices.
