Class 12 NCERT Solutions- Mathematics Part I - Chapter 3 Matrices - Exercise 3.4 | Set 2

Matrices are a fundamental concept in mathematics providing a compact way to represent and manipulate data and equations. They are used in various fields including algebra, calculus, and applied mathematics. This chapter focuses on the operations and properties of matrices essential for solving the systems of linear equations and performing transformations in vector spaces.

Matrices

A matrix is a rectangular array of numbers arranged in rows and columns. Each number in the matrix is called an element. The Matrices are used to represent linear transformations and systems of the linear equations efficiently. The basic operations on the matrices include addition, subtraction, multiplication, and finding the determinant and inverse. Understanding these operations is crucial for solving complex mathematical problems and real-world applications.

Exercise 3.4 of Chapter 3 in Class 12 NCERT Mathematics Part I further explores the concepts of matrices, building upon the foundational knowledge established earlier. This set delves deeper into matrix operations, properties, and applications, challenging students with more complex problems. It emphasizes advanced matrix manipulations, including solving matrix equations, working with special matrices like orthogonal matrices, and exploring the relationships between matrix operations and their inverses. This exercise set aims to enhance students' analytical skills and prepare them for applying matrix concepts in various fields of mathematics and science.

The content of this article has been merged with Chapter 3 Matrices - Exercise 3.4 as per the revised syllabus of NCERT.

Question 11. 

Solution:

}

Question 12. 

Solution:

Here, both the elements of R₂ of L.H.S. are 0.

Therefore, A^-1 does not exist.

Question 13. 

Solution:

Question 14. 

Solution:

Here, both the elements of R2 of L.H.S. are 0.

Therefore, A-1 does not exist.

Question 15. 

Solution:

Let A= 

W.K.T. , A=IA

Therefore, A^-1 =

Question 16. 

Solution:

Let A=

W.K.T. , A=IA

Question 17. 

Solution:

Let A=

W.K.T. , A=IA

Question 18. Matrices A and B will be inverse of each other only if:

(A) AB = BA  

(B) AB = BA = 0

(C) AB = 0, BA = I

(D) AB = BA = I

Solution:

According to the definition of inverse of square matrix,

Option (D) is correct

 i.e. AB=BA=I

Summar

This set of questions in Exercise 3.4 provides a comprehensive exploration of advanced matrix concepts. It covers a wide range of topics including orthogonal matrices, matrix equations, properties of matrix operations, and special matrices. The problems require students to apply their understanding of matrix multiplication, transposition, and inversion in various contexts. By solving these questions, students develop a deeper intuition for matrix algebra, enhancing their problem-solving skills and preparing them for more advanced mathematical concepts in linear algebra and its applications in fields such as computer science, physics, and engineering.

• Matrix Multiplication
• Determinants of Matrices
• Inverse of a Matrix