NCERT Solutions for Class 12 Maths Chapter 4 Determinants

 

NCERT Solutions for Class 12 Maths Chapter-4 Determinants

In our previous chapter we already study about matrices and also algebra of matrices. In this chapter we will study determinants and their properties. Determinant is an important part of matrices. In this chapter we deal with determinants of order upto three only. In this chapter there are 6 exercises with 68 questions in them. The NCERT Solutions for Class 12 Maths Chapter-4 Determinants are prepared and explained by our subject experts for the students.

What are the Determinants?

To every square matrix A=\left [ a_{ij} \right ] of order n, we can associate a number (real or complex) called determinant of the square matrix A. Let's take a determinant (A) of order two-

If A is a then the determinant of A is written as |A|=matrix  

A=\begin{bmatrix} a &b\\ c & d \end{bmatrix},         |A| =\begin{vmatrix} a & b\\ c& d \end{vmatrix}=det(A)

det(A)=|A| =\Delta =\begin{vmatrix} a_{11} & a_{12}\\ a_{21}& a_{22} \end{vmatrix}=a_{11}a_{22}-a_{21}a_{12}

The six exercises of this NCERT Class 12 Maths Chapter 4 Determinants covers the properties of determinants, cofactors and applications like finding the area of triangle, solutions of linear equations in two or three variables, minors, consistency and inconsistency of system of linear equations, adjoint and inverse of a square matrix, and solution of linear equations in two or three variables using inverse of a matrix. In Maths Chapter 4 Determinants, NCERT textbook explained every concept in detail with solved examples.

Topics and sub-topics of NCERT Grade 12 Maths Chapter-4 Determinants-

4.1 Introduction

4.2 Determinant

4.2.1 Determinant of a matrix of order one

4.2.2 Determinant of a matrix of order two

4.2.3 Determinant of a matrix of order 3 × 3

4.3 Properties of Determinants

4.4 Area of a Triangle

4.5 Minors and Cofactors

4.6 Adjoint and Inverse of a Matrix

4.7 Applications of Determinants and Matrices

4.7.1 Solution of a system of linear equations using the inverse of a matrix

Some examples are-

Que.1 Evaluate the following determinant-

             \begin{vmatrix} 2 & 4\\ -5 & -1\end{vmatrix} 

Solution-

\begin{vmatrix} 2 & 4\\ -5 & -1\end{vmatrix} = 2(-1) - 4(-5) = -2 + 20 = 18

 

Que.2 Evaluate the following determinant-

           \begin{vmatrix} \cos \theta & -\sin \theta \\ \sin \theta &\cos \theta \end{vmatrix}

Solution-

\dpi{100} \begin{vmatrix} \cos \theta & -\sin \theta \\ \sin \theta &\cos \theta \end{vmatrix} = cos \theta (\cos \theta) - (-\sin \theta)\sin \theta = \cos^2\theta + \sin ^2 \theta = 1

NCERT Solutions for Class 12 Maths Chapter 4 Determinants- Solved Exercise Questions

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.1

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.2

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.3

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.4

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.5

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.6

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous

NCERT Solutions for class 12- Maths

Chapter 1

Relations and Functions

Chapter 2

Inverse Trigonometric Functions

Chapter 3

Matrices

Chapter 5

Continuity and Differentiability

Chapter 6

Application of Derivatives

Chapter 7

Integrals

Chapter 8

Application of Integrals

Chapter 9

Differential Equations

Chapter 10

Vector Algebra

Chapter 11

Three Dimensional Geometry

Chapter 12

Linear Programming

Chapter 13

Probability

NCERT Solutions for Class 12

 

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