# 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-

$\dpi{100} \begin{vmatrix} 2 & 4\\ -5 & -1\end{vmatrix}$

Solution-

$\dpi{100} \begin{vmatrix} 2 & 4\\ -5 & -1\end{vmatrix} = 2(-1) - 4(-5) = -2 + 20 = 18$

Que.2 Evaluate the following determinant-

$\dpi{100} \begin{vmatrix} \cos \theta & -\sin \theta \\ \sin \theta &\cos \theta \end{vmatrix}$

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