## Exercise 4.1 ncert math solution class 11

Chapter 4:(Principle Of Mathematical Induction) Prove the following by using the principle of mathematical induction for all n ∈ N (Exercise 4.1 ncert math solution class 11) Question 1:- Solution: Let be the given statement For , Assume that is true for some positive integer , such that We will now prove that is also … Read more

## class 12 maths exercise 4.5 ncert solution

EXERCISE 4.5 (Determinant) class 12 maths exercise 4.5 ncert solution Question 1: Find the adjoint of the matrix Solution: Let Then, Thus Question 2: Find the adjoint of the matrix Solution: Let Then, Question 3:  Verify for Solution: Let Then, Also, Now, Hence, Now, Also, Hence, . Question 4: verify for Solution : Let Then … Read more

## Class 12 ncert solution math exercise 4.3 determinants

EXERCISE 4.3 (Determinants) Question 1: Find area of the triangle with vertices at the point given in each of the following:(Class 12 ncert solution math exercise 4.3 determinants) (i) (ii) (iii) Solution: (i) The area of the triangle with vertices is given by the relation, Hence, area of the triangle is square units. (ii) … Read more

## Class 12 ncert solution math exercise 4.6

EXERCISE 4.6 ( Determinants ) Question 1: Examine the consistency of the system of equations:(Class 12 ncert solution math exercise 4.6) Solution: The given system of equations is: The given system of equations can be written in the form of , where Hence, =3-4 So, is non-singular. Therefore, exists. Thus, the given system … Read more

## Class 12 ncert solution math exercise 4.1

EXERCISE 4.1 ( Determinants ) Evaluate the determinant:(Class 12 ncert solution math exercise 4.1) Question 1:   Solution: Let Hence, Question 2: Evaluate the determinants: (i) (ii) Solution: (i) (ii) Question 3: If , then show that Solution: The given matrix is Therefore, Hence, Now, Therefore, Thus, proved. Question 4: If , then show … Read more

## Class 12 ncert solution math exercise 4.4

EXERCISE 4.4 (Determinants) Write Minors and Cofactors of the elements of following determinants:(Class 12 ncert solution math exercise 4.4) Question 1: (i) (ii) Solution: (i) The given determinant is Minor of element is minor of element minor of element minor of element minor of element Cofactor of is (ii) The given determinant is Minor of … Read more