Matrices

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Class 12 Maths Chapter 3
Matrices
Important Questions

Preparing for the Class 12 Maths exams, specifically Chapter 3 on Matrices, holds pivotal significance in establishing a solid mathematical groundwork. This chapter delves into the world of matrices, exploring their properties, operations, and applications across various disciplines. To excel in this chapter, it’s imperative to acquaint oneself with crucial questions specifically designed to gauge comprehension of the fundamental concepts. Here are some class 12 matrices important questions and answers. These questions serve as benchmarks to test knowledge and understanding. Embracing a diverse range of question formats aids in navigating uncertainties, ensuring comprehensive readiness for the impending exams

Table of Contents

Introduction

Matrices are a fundamental concept in mathematics and have numerous applications in various fields such as engineering, physics, computer science, and economics. Matrices are usually denoted by uppercase letters (e.g., A, B, C) and their elements are often denoted by lowercase letters with subscripts, providing a comprehensive understanding through matrices class 12 questions and answers. These are matrices important questions which will pave the way for a thorough exploration of this crucial aspect of mathematics syllabus.

What are Matrices?

Matrices are a key concept in mathematics, particularly in the field of linear algebra. A matrix is a rectangular arrangement of numbers, symbols, or expressions, organized in rows and columns. These numbers can represent data or mathematical functions.

Elements: Each individual number in a matrix is called an element.
Rows and Columns: The horizontal lines are rows, and the vertical lines are columns.
Size: The size of a matrix is defined by its number of rows and columns, typically noted as
m×n (m rows and n columns).

Class 12 Matrices Important Questions and Answers

Q1. The number of all possible matrices of order 2 × 3 with each entry 0 or 1 is:

Options

(a) 64
(b) 12
(c) 36
(d) 28

Ans. (a) 64
Explanation:
In a 2 X 3 matrix, the number of elements is 6.
Each place could have 2 elements.
Total possible outcomes = 2 x 2 x 2 x 2 x 2 = 64

Q2. If A and B are symmetric matrices of the same order, then (AB– BA) is a:

Options

(a) Skew symmetric matrix
(b) Null matrix
(c) Symmetric matrix
(d) None of these

Ans. (a) Skew symmetric matrix

Explanation:
Since A and B are symmetric matrices such that A′ = A and B′ = B
(AB - BA)′ = (AB)′ - (BA)′
= B′A′ - A′B′
= BA - AB
= - (AB - BA)
Hence, (AB– BA) is a skew symmetric matrix.

Q3. What are scalar and diagonal matrix ?

Explanation:
A scalar matrix refers to a square matrix in which the diagonal elements are equal and every non-diagonal element is zero.
A diagonal matrix is referred to as a square matrix , provided all the elements except the elements in the leading diagonals are zero.

Q4. What is the value of every diagonal element of a skew matrix?

Explanation:
In the skew matrix, ,every diagonal element is zero for the square matrices.

Q5. What are the possible orders if a matrix has 28 elements?

Explanation:
The possible orders are
1 x 28, 2 x 14, 4 x 7, 7 x 4, 14 x 2, 28 x 1.

CBSE Class 12 Maths Chapter wise Important Questions

Chapter No.	Chapter Name
Chapter 1	Relations and Functions
Chapter 2	Inverse Trigonometric Functions
Chapter 3	Matrices
Chapter 4	Determinants
Chapter 5	Continuity and Differentiability
Chapter 6	Applications of Derivatives
Chapter 7	Integrals
Chapter 8	Applications of the Integrals
Chapter 9	Differential Equations
Chapter 10	Vectors
Chapter 11	Three - dimensional Geometry
Chapter 12	Linear Programming
Chapter 13	Probability

Conclusion

The concepts of relations and functions are integral to the understanding of mathematical principles and are widely applied in various fields of study. Exploring cbse class 12 maths matrices important questions, becomes essential for a comprehensive grasp of this fundamental aspect of mathematics.. To enhance understanding, platforms like Oswal.io provide a wealth of resources, including question-answer sets, comprehensive class 12 questions and answers.Utilising these resources ensures students acquire the knowledge necessary to excel in their studies and examinations, inviting them to delve deeper into the captivating realm of matrices.

Frequently Asked Questions

Q1 : What is a Matrix?

Ans: A matrix is a rectangular array of numbers, symbols, or expressions, organized in rows and columns. It is a fundamental concept in mathematics and is used in various fields for representing and manipulating data.

Q2 : How Do You Add or Subtract Matrices?

Ans: To add or subtract matrices, they must be of the same size. You add or subtract corresponding elements from each matrix. For instance, the element in the first row and first column of Matrix A is added to or subtracted from the element in the same position in Matrix B.

Q3 : What is Matrix Multiplication?

Ans: Matrix multiplication involves multiplying two matrices. The number of columns in the first matrix must equal the number of rows in the second. The resulting matrix has the same number of rows as the first matrix and the same number of columns as the second matrix.

Q4 : What is an Identity Matrix?

Ans: An identity matrix is a square matrix with ones on the diagonal and zeros elsewhere. It’s the multiplicative identity in matrix algebra, meaning any matrix multiplied by an identity matrix of compatible size remains unchanged.

Q5: What is the Determinant of a Matrix?

Ans: The determinant is a scalar value that can be computed from a square matrix. It provides important properties about the matrix, such as whether it has an inverse and the volume distortion during the linear transformation the matrix represents.

Chapter Wise Important Questions for CBSE Board Class 12 Maths
Relations and Functions
Inverse Trigonometric Functions
Matrices
Determinants
Continuity and Differentiability
Applications of Derivatives
Integrals
Applications of the Integrals
Differential Equations
Vectors
Three - dimensional Geometry
Linear Programming
Probability

Class 12 Maths Chapter 3 Matrices Important Questions

Introduction

What are Matrices?

Class 12 Matrices Important Questions and Answers

Q1. The number of all possible matrices of order 2 × 3 with each entry 0 or 1 is:

Options

(a) 64 (b) 12 (c) 36 (d) 28

Q2. If A and B are symmetric matrices of the same order, then (AB– BA) is a:

Options

(a) Skew symmetric matrix (b) Null matrix (c) Symmetric matrix (d) None of these

Q3. What are scalar and diagonal matrix ?

Q4. What is the value of every diagonal element of a skew matrix?

Q5. What are the possible orders if a matrix has 28 elements?

CBSE Class 12 Maths Chapter wise Important Questions

Conclusion

Frequently Asked Questions

Q1 : What is a Matrix?

Q2 : How Do You Add or Subtract Matrices?

Q3 : What is Matrix Multiplication?

Q4 : What is an Identity Matrix?

Q5: What is the Determinant of a Matrix?

Class 12 Maths Chapter 3
Matrices
Important Questions

(a) 64
(b) 12
(c) 36
(d) 28

(a) Skew symmetric matrix
(b) Null matrix
(c) Symmetric matrix
(d) None of these