Class 12 Maths Chapter 4 – Determinants NCERT Solutions – FREE PDF Download | Hand – Written Notes

Chapter 4 Determinants is one of the most important and scoring chapters of the Class 12 Maths NCERT syllabus. This chapter is closely related to Matrices and is widely used in solving linear equations, higher mathematics, and real-life problems.

At Edu Tehri, this chapter is explained with clear theory, step-by-step NCERT solutions, handwritten notes, important formulas, and free PDFs, making it easier for students to understand and score well in exams.

Important Topics of Chapter 4

The following topics are included in NCERT Chapter 4 – Determinants:

1. Determinant of a matrix
2. Determinant of a 2 × 2 matrix
3. Determinant of a 3 × 3 matrix
4. Properties of determinants
5. Minors and cofactors
6. Expansion of determinants
7. Adjoint of a matrix
8. Inverse of a matrix using adjoint
9. Applications of determinants
10. Solving linear equations using determinants

These topics are frequently asked in board exams and are very important for competitive exams as well.

Important Formulas – Chapter 4

Download Important Formula - Free PDF

Formulas play a key role in this chapter. Students should practice them regularly.

Properties of Determinants

If any two rows or columns are equal, then determinant = 0

Interchanging two rows or columns changes the sign of determinant

If one row or column is multiplied by a constant k, determinant also gets multiplied by k

If one row or column is zero, determinant = 0

Minor and Cofactor

Minor of element aᵢⱼ is denoted by Mᵢⱼ
Cofactor of element aᵢⱼ is Cᵢⱼ = (−1)ᶦ⁺ʲ Mᵢⱼ

Adjoint and Inverse

adj(A) = transpose of cofactor matrix
A⁻¹ = adj(A) / |A|, if |A| ≠ 0

Solution of Linear Equations

A system of equations has:

• Unique solution if |A| ≠ 0
• No solution or infinitely many solutions if |A| = 0

Exercise 4.1 – Determinants of 2 × 2 Matrices

This exercise covers:

• Finding determinants
• Basic properties

Question Type:

• Direct numerical questions

Exam Weightage: Useful for 1–2 marks

Exercise 4.2 – Determinants of 3 × 3 Matrices

This exercise focuses on:

• Expansion of determinants
• Simplification

Exam Weightage: High

Exercise 4.3 – Properties of Determinants

This exercise includes:

• Proving properties
• Simplification using properties

Exam Weightage: Very High

Exercise 4.4 – Adjoint and Inverse

This exercise covers:

• Finding adjoint
• Finding inverse of matrices

Exam Weightage: Very Important

Exercise 4.5 – Applications of Determinants

This exercise focuses on:

• Solving linear equations
• Application-based questions

Exam Weightage: High for 5-mark questions

Key Features of Chapter 4

• Very high exam weightage
• Concept + calculation based chapter
• Closely related to matrices
• Useful in higher mathematics
• Scoring if practiced properly

With Edu Tehri’s structured explanations and handwritten notes, students can master this chapter easily.

Frequently Asked Questions (Long Answer Type – NCERT Based)

Q1. What is a determinant?

A determinant is a numerical value associated with a square matrix that helps in solving linear equations and finding the inverse of a matrix.

Q2. When does a matrix have an inverse?

A matrix has an inverse only when its determinant is not equal to zero.

Q3. What happens if determinant is zero?

If the determinant is zero, the matrix is singular and does not have an inverse.

Q4. What is the importance of adjoint of a matrix?

Adjoint is used to find the inverse of a matrix and to solve linear equations.

Q5. How many solutions can a system of equations have?

It can have:

• One unique solution
• No solution
• Infinitely many solutions

Q6. Is Chapter 4 important for board exams?

Yes, it is one of the most important chapters with high weightage.

Q7. Which exercise is most important in this chapter?

Exercises 4.3, 4.4, and 4.5 are most important for exams.

Q8. Are NCERT questions enough to score well?

Yes, board exam questions are mostly based on NCERT exercises.

Q9. Is this chapter difficult?

It may seem lengthy, but with regular practice, it becomes easy.

Q10. Where can students get free NCERT solutions for Determinants?

Students can get free NCERT solutions, handwritten notes, and PDFs on Edu Tehri.

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