Important Questions for CBSE Class 12 Maths Chapter 3 - Matrices 2024-25

The Class 12 Maths Matrices important questions are all about learning the basics and deriving solutions of complex problems by practising often. Matrices important questions include its order, zero and identity matrix, operations of a matrix, transpose of a matrix, elementary row and columns operations and so on.  Vedantu has curated a place where you can find Class 12 Maths Chapter 3 important questions at your disposal, easily. The aim is for students to solve all the problems related to Matrices Class 12 important questions, effortlessly. 

Class 12 Maths Chapter 3 Matrices

Introduction

A Matrix is defined as a rectangular arrangement of numbers (can be either real or complex) and it is enclosed by  ( ) or [ ] or | |. There are a few types of matrices that you should know about. 

Types of Matrices

1. Column Matrix: Column matrix has any number of rows and only one column.

2. Row Matrix: Row matrix has any number of columns and only one row. 

3. Horizontal Matrix: Horizontal matrix is one which the number of rows is lower than the number of columns.

4. Vertical Matrix: It is a type of matrix where the number of rows is higher than the number of columns.  

5. Square Matrix: A square matrix is a matrix of an order mn, such that m=n.

6. Rectangular Matrix: A rectangular matrix is a matrix of an order mn, such that m   n.

7. Null/Zero Matrix: It is a matrix of any order that has zero as all its elements.

8. Scalar Matrix: A scalar matrix refers to a square matrix in which the diagonal elements are equal and every non-diagonal element is zero.

9. Diagonal Matrix: A diagonal matrix is referred to a square matrix where A=[aⱼₖ]ₘₓₙ, provided all the elements except the elements in the leading diagonals are zero. 

10. Principal Diagonal of a Matrix: Ina square matrix, the first diagonal element of the first row to the last diagonal element of the last row is known as the principal diagonal of a matrix. 

11. Identity/Unit Matrix: Identity matrix also refers to a square matrix in which every diagonal element is equal to 1 and every non-diagonal element is zero. 

12. Singular Matrix: A singular matrix is a square matrix A when the determinant of A is denoted by det (A) or |A| is zero which means, |A|= 0 if otherwise, it is known as a non-singular matrix. 

13. Equal Matrices: Two matrices for suppose, A and B are said to be equal if the corresponding elements of the matrices are all equal and both have the same order. 

Matrix Algebra

1. Matrix Multiplication by Scalar 

If 𝑙be any scalar and A=[aⱼₖ]ₘₓₙ, then the matrix which is obtained by multiplying each of the elements of A by 𝑙and it is denoted by 𝑙A,

Where lA=[laⱼₖ]ₘₓₙ

2. Matrix Addition

Let us take A and B two matrices having each of order mn. Therefore, the sum of those matrices A+B is defined, given the matrices A And B are of the same order. 

If A=[aⱼₖ]ₘₓₙ, B=[𝑏ⱼₖ]ₘₓₙ

Then, A+B=[aⱼₖ+𝑏ⱼₖ]ₘₓₙ

Properties of Matrix Addition: Let us take A, B and C are three matrices of order mn

Then, 

As per Commutative Law, A+B=B+A

As per Associative Law, (A+B)+C=A+(B+C)

Existence of Additive Identity: An additive identity is a zero matrix (0) of the order mn (same as of A)

If A+0=A=0+A

Existence of Additive Inverse: An additive inverse where A is a square matrix, then the matrix is (-A)

If A+(-A)=0=(-A)+A

Cancellation Law:

If the product of matrix A and matrix B is equal to the product of matrix A and matrix C, and matrix A is invertible, then matrix B and matrix C must be equal. 

A+B=A+CB=C (left cancellation law)

B+A=C+AB=C (right cancellation law)

3. Matrix Subtraction

Let us take A and B which are the two matrices of the same order,

If A=[aⱼₖ]ₘₓₙ, B=[bⱼₖ]ₘₓₙ

then the subtraction of those matrices, 

A-B=[aⱼₖ - bⱼₖ]]ₘₓₙ 

Some Ch 3 Maths Class 12 Important Questions

Question 1. Define Square Matrix.

Ans: A square matrix is a matrix in which the number of rows is equal to the number of columns, ie., m=n.

Question 2. What is the Value of Every Diagonal Element of a Skew Matrix?

Ans: Zero.

Question 3. What Are the Possible Orders If a Matrix Has 28 Elements?

Ans: The possible orders are denoted by

1 x 28, 

2 x 14, 

4 x 7, 

7 x 4, 

14 x 2,

28 x 1

Did You Know?

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Matrices can be a helpful way to represent a study related to linear maps between the spaces of a finite-dimensional vector. 

Why Choose Vedantu?

Vedantu has gathered an array of experts in the field of all subjects to curate a syllabus and a list of important questions especially for you. Class 12 Matrices important questions are necessary for the students because it consists of an important part of the Class 12 Maths Syllabus. Nowadays, especially after the pandemic happened, most students have resorted to online learning. At such a crucial time, quality online learning is very important and students require quality places where they can learn online. 

A student needs to plan if the goal is to attain a good score in the final examination. To plan strategically, one needs to note down all the important questions related to the subject matter. Matrices important questions are provided here in a comprehensive list in a specific order so that a student can understand and learn it, quickly. Comprehensive planning will provide the students with a set aim to achieve all their requirements even in a limited amount of time. 

Matrices Class 12 important questions are required for those students who are nearing their Class 12 final exams. They might need to wrap up their syllabus quickly within a limited amount of time. These important questions will help them focus throughout their study schedule to determine what is best for them. Ultimately, the goal is to learn and score good and Vedantu provides all the solutions that are required to reach this goal. 

Important Related Links for CBSE Class 12 Maths 

Conclusion

Matrix has a long history of representing elements in solving linear equations. It can be used to write and study multiple linear equations simultaneously, which are referred to as a system of linear equations. In mathematics, a matrix is denoted by an array of numbers, expressions and symbols, arranged neatly in rows and columns. All the horizontal and vertical lines represented in a matrix are known as rows and columns. 

The individual-specific items that are denoted by numbers, expressions and symbols are known as the elements or entries of a matrix. Two matrices of the same size can be added and/or subtracted element by element. However, two matrices can only be multiplied when the number of columns in the first is equal to the number of rows in the second. 

The matrix can be used in machine learning algorithms too. To reach the complexity level where you can start studying machine learning algorithms represented by a matrix, one needs to get their basics right. First of all, a student of class 12 needs to strengthen their base in the matrix applications and thereby, focus on the topic to learn more. 

Application of some special matrices is also important for the syllabus of Class 12 Maths Chapter 3. These special matrices are clearly defined here for the convenience of students so that they can apply these special matrices in more complex equations. Understanding these special matrices will help in understanding a deep-rooted knowledge of the subject. 

Class 12 Matrices important questions will help you learn and dive deep into the world of matrices. The pressure seems real when Class 12 final exams and nearby and you have a lot to mug up. While rote learning can be an easy way out, but it takes time and effort to learn and understand something. The skills and knowledge you derive by understanding a subject in its entirety can help you a long way in the future. The reasons why important questions for Class 12 Chapter 3 Matrices are curated here for your convenience.