Matrices Question Answers: NCERT Class 12 Mathematics

Welcome to the Chapter 3 - Matrices, Class 12 Mathematics - NCERT Solutions page. Here, we provide detailed question answers for Chapter 3 - Matrices.The page is designed to help students gain a thorough understanding of the concepts related to natural resources, their classification, and sustainable development.

Our solutions explain each answer in a simple and comprehensive way, making it easier for students to grasp key topics and excel in their exams. By going through these Matrices question answers, you can strengthen your foundation and improve your performance in Class 12 Mathematics. Whether you're revising or preparing for tests, this chapter-wise guide will serve as an invaluable resource.

Matrix is one of the most fundamental chapters of Mathematics, which will help us not only in mathematics but also in other branches like mechanics, optics, computer science, etc. It solves tedious calculations very easily. Topics incorporated in this chapter are notation, order, types and equality of matrix, zero matrix, transpose, symmetric and skew symmetric matrices, addition and multiplication of matrices, properties, row and column operations, Invertible matrices and proof of uniqueness of inverse, if it exists.

Download PDF - Chapter 3 Matrices - Class 12 Mathematics

Download PDF - NCERT Examplar Solutions - Chapter 3 Matrices - Class 12 Mathematics

Exercise 1

  • Q2 If a matrix has 24 elements, what are the possible order it can have? What, if it has 13 elements?
    Ans:

    We know that if a matrix is of the order m × n, it has mn elements. Thus, to find all the possible orders of a matrix having 24 elements, we have to find all the ordered pairs of natural numbers whose product is 24.

    The ordered pairs are: (1, 24), (24, 1), (2, 12), (12, 2), (3, 8), (8, 3), (4, 6), and
    (6, 4)

    Hence, the possible orders of a matrix having 24 elements are:

    1 × 24, 24 × 1, 2 × 12, 12 × 2, 3 × 8, 8 × 3, 4 × 6, and 6 × 4

    (1, 13) and (13, 1) are the ordered pairs of natural numbers whose product is 13.

    Hence, the possible orders of a matrix having 13 elements are 1 × 13 and 13 × 1.


    Q3 If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?
    Ans:

    We know that if a matrix is of the order m × n, it has mn elements. Thus, to find all the possible orders of a matrix having 18 elements, we have to find all the ordered pairs of natural numbers whose product is 18.

    The ordered pairs are: (1, 18), (18, 1), (2, 9), (9, 2), (3, 6,), and (6, 3)

    Hence, the possible orders of a matrix having 18 elements are:

    1 × 18, 18 × 1, 2 × 9, 9 × 2, 3 × 6, and 6 × 3

    (1, 5) and (5, 1) are the ordered pairs of natural numbers whose product is 5.

    Hence, the possible orders of a matrix having 5 elements are 1 × 5 and 5 × 1.


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