Class 12 Math Determinants NCERT/Grade 12
Welcome to the Class 12 Math Determinants NCERT/Grade 12 chapter! Determinants help us understand how a matrix behaves — whether it stretches space, flips shapes, collapses into a line, or produces a unique solution to a system of equations.
In this chapter, you’ll explore minors, cofactors, adjoint, inverse of a matrix, and applications in solving linear equations. From simple 2×2 determinants to more advanced 3×3 expansions, each step reveals how powerful and useful determinants are in mathematics.
What You Will Learn
- Understanding 2×2 and 3×3 determinants
- Minors and Cofactors
- Adjoint of a Matrix
- Finding the Inverse of a Matrix
- Area of Triangle using Determinants
- Solving Linear Equations using Matrix Method
Quick Example
| a b |
| c d | Determinant = ad − bc
This single number (the determinant) tells us whether a matrix has an inverse, whether a system of equations has a unique solution, and much more.
📄 Download NCERT Determinants PDFClass 12 Math Determinants NCERT/Grade 12
Exercise 4.1 Determinants
SOLUTION 4.1
Exercise 4.2 Area Of Triangle
Solution 4.2
EXERCISE 4.3 – Minors & Cofactors
Solution 4.3
EXERCISE 4.4 – Adjoint and Inverse
EXERCISE 4.5 – Applications / Matrix Method
📍 Check Consistency (Questions 1 to 6)
Conclusion — Class 12 Math Determinants (NCERT / Grade 12)
The chapter Determinants is a compact, powerful tool in linear algebra that connects geometry, systems of linear equations, and matrix theory. From simple 2×2 determinants to 3×3 expansions, mastering minors, cofactors, adjoint and inverse helps you:
- Decide invertibility: a non-zero determinant means a matrix has an inverse.
- Solve systems efficiently: use matrix inverse (AX = B) or expansion methods for exact solutions.
- Compute areas: determinant formula gives area of a triangle from vertex coordinates.
- Understand transformations: determinants measure how linear maps scale and orient area/volume.
Exam tip: always look for rows or columns with zeros to simplify expansion, and remember the sign pattern \((−1)^{i+j}\) when forming cofactors. Practice using both expansion and the adjoint method to gain speed and confidence.
— Keep practicing step-by-step expansions and matrix inverses. Good luck with your Class 12 preparations!
The chapter Determinants in Class 12 Mathematics forms a core part of higher-level algebra and plays a crucial role in understanding matrices, linear equations, and advanced mathematical concepts used in engineering and other competitive exams. By practising regularly and studying well-structured solutions, students can develop strong analytical skills and improve speed and accuracy in problem solving. The concepts of minors, cofactors, adjoint, inverse of matrices, and properties of determinants become much easier when learned through consistent revision and solved examples.
For deeper clarity, students should also refer to official NCERT materials to strengthen conceptual understanding and ensure they follow the CBSE exam pattern precisely. You can access the official textbook and additional resources here:
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NCERT Official Website – Class 12 Mathematics Textbook (Determinants Chapter)
https://ncert.nic.in