NCERT Solutions for Maths Class 12 Chapter 3 Matrices Exercise 3.4 - FREE PDF Download
NCERT Solutions for Maths Exercise 3.4 Class 12 Chapter 3 - Matrices explains the fundamental ideas of matrices in detail. This exercise covers fundamental topics such as matrix multiplication, matrix operation properties, and how to find a matrix's inverse. The step-by-step solutions will make students easy to understand these concepts completely.
- 3.1Exercise 3.4
It is important to concentrate on every type of matrix operation and understand its applications. NCERT Solutions for Maths Class 12 will help to improve student's knowledge and problem-solving skills, which are required for your board exams. Start practising from the start by downloading the FREE CBSE Class 12 Maths Syllabus.
Glance on NCERT Solutions Maths Chapter 3 Exercise 3.4 Class 12 | Vedantu
Exercise 3.4 Class 12 explains invertible matrices, which are matrices that have an inverse. An invertible matrix is a square matrix with a non-zero determinant.
If a matrix A is invertible, there is another matrix B such that AB = BA = I, where I is the identity matrix.
It is important to understand the properties of invertible matrices, including that the product of two invertible matrices is also invertible.
The inverse of a product of matrices is the product of their inverses in the reverse order.
Another key point is that a matrix is invertible if and only if it is row-equivalent to the identity matrix, meaning it can be transformed into the identity matrix using row operations.
Additionally, the inverse of a matrix is unique. If a matrix has more than one inverse, it is not considered invertible.
If A is an invertible matrix, the system of linear equations Ax = b has a unique solution given by x =$A^{-1}b$.
There is only one solved question in Chapter 3 Ex 3.4 Class 12 Matrices.
FAQs on NCERT Solutions for Class 12 Maths Chapter 3 - Matrices Exercise 3.4
1. Where can I find NCERT Solutions for Maths Chapter 3 Matrices Ex 3.4 Class 12?
Vedantu, India’s top e-learning site, provides NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.4 Class 12. It is available in a free-to-download PDF format. Exercise-wise NCERT Solutions for Chapter 3 Matrices are curated by subject matter experts at Vedantu. The material aids in effective exam preparation as well as clearing the fundamentals of the chapter. NCERT Solutions for Maths Chapter 3 Ex 3.4 Class 12 are based on the latest NCERT guidelines and exam patterns. Hence, students can avail them to score well in the exams. The exercise’s solutions help students to get a thorough knowledge of the chapter and simple explanations of the problems.
2. How are NCERT Solutions for Maths Chapter 3 Matrices Ex 3.4 Class 12 helpful?
The online Class 12 Maths Ex 3.4 Solutions Matrices are prepared for doubt resolution and exam preparation. It is of great importance to learn the exercise well and provide confidence to solve the problems. These are prepared by experts who have immense knowledge and experience. Hence, students can get a detailed explanation of the problems in an easy-to-understand manner. NCERT Solutions for CBSE Maths Chapter 3 Ex 3.4 Class 12 can be utilized by students to solve their doubts regarding the exercise. NCERT Solutions for Class 12 Chapter 3 Matrices for Exercise 3.4 improves your chances of scoring well in the exam.
3. What are the elementary operations of a Matrix in Exercise 3.4 Class 12 Maths?
There are six elementary operations of a Matrix (3 due to rows and 3 due to columns). The elementary operations of a Matrix are also called the Transformation of a Matrix. Following are the elementary operations or transformations of a matrix:
The interchange of any two rows or two columns
The multiplication of the elements of any row or column by a non-zero number
The addition to the elements of any row or column, the corresponding elements of any other row or column multiplied by any non-zero number.
4. Why does a rectangular matrix not possess an inverse matrix in Exercise 3.4 Class 12 Maths?
A rectangular matrix does not possess an inverse matrix since for the products BA and AB to be defined as equal, matrices A and B must be square matrices of the same order.
5. How important is Exercise 3.4 Class 12 Maths?
Exercise 3.4 Class 12 Maths is an important exercise from an exam point of view. It is not only important for board exams but also for competitive exams. Students of Class 12 should understand the basic concepts given in the exercise to solve the questions. NCERT Solutions of Chapter 3 of Class 12 Maths can help students get an in-depth understanding of the basic concepts and ideas for solving the questions given in the exercise easily. They can practice questions from the textbook and score good marks in Class 12 Maths.
6. What are the important points given in Exercise 3.4 Class 12 Maths?
In Class 12 Maths Ex 3.4 Solutions, students will study the following important points:
Six elementary operations on matrices out of which three are due to rows and three due to columns.
What are invertible matrices? It is an important concept of matrices that students will be able to understand by solving different types of questions given in Exercise 3.4
Why a rectangular matrix is not an inverse matrix
Using elementary operations to find the inverse of a matrix.
7. How much time will I need to prepare Class 12 Maths Ex 3.4 Solutions for my exams?
Students have to focus on the main concepts given in Exercise 3.4 of Chapter 3 of Class 12 Maths. For Exercise 3.4 of Class 12 Maths they have to spend 20 minutes to solve the question given in the exercise. The time may vary from student to student depending on different factors such as capability, efficiency, and speed of the students. Students can also get help from the NCERT Class 12 Maths Ex 3.4 Solutions given on Vedantu.
8. How many theorems are related to the inverse of matrix Class 12 Maths Ex 3.4 Solutions?
Two theorems are related to Exercise 3.4 based on the inverse of a matrix. Theorem three states the uniqueness of inverse which means that the inverse of a square matrix is unique if it exists and theorem four which states that if A and B are invertible matrices having the same order, then (AB)⁻¹ = B⁻¹ A⁻¹. Students can understand the theorems by solving the textbook questions given in Exercise 3.4. Students can get solutions for all textbook questions for Exercise 3.4 on Vedantu.
9. What are invertible matrices, and why are they important in Exercise 3.4 Maths Class 12?
Invertible matrices, also known as non-singular matrices, have an inverse such that when multiplied by their inverse, they yield the identity matrix. They are important in Exercise 3.4 because understanding their properties is crucial for solving complex matrix problems and applications in linear algebra.
10. How can I determine if a matrix is invertible in Exercise 3.4 Maths Class 12?
A matrix is invertible if it is a square matrix with a non-zero determinant. Additionally, if a matrix can be row-reduced to the identity matrix through elementary row operations, it is also considered invertible.
11. What methods are used to find the inverse of a matrix in Exercise 3.4 Maths Class 12?
Exercise 3.4 covers methods such as the adjoint method and row reduction to find the inverse of a matrix. These methods help in systematically determining the inverse, which is essential for solving linear equations and other matrix-related problems.
12. How is the concept of matrix inversion applied to solve linear equations in Exercise 3.4 Maths Class 12?
If a matrix A is invertible, the system of linear equations represented by Ax = b can be solved using the inverse of the matrix. The unique solution is given by x = A^(-1)b, where A^(-1) is the inverse of matrix A. This application is highlighted in Exercise 3.4 to demonstrate the practical use of matrix inversion in solving equations.