Chapter 7 of 27
Revision Notes
Determinants — Revision Notes
KEAM · Mathematics
Free Determinants revision notes for KEAM Mathematics 2026 — key concepts, formulas, and definitions for quick revision.
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Key concepts, formulas, and definitions from Determinants for KEAM Mathematics preparation.
Key Topics to Revise
1
Introduction to Determinants
- Determinant is a numerical value associated with every square matrix
- Denoted by |A|, det(A), or Δ (delta)
- Only defined for square matrices (n×n)
2
Properties of Determinants
- If two rows (or columns) are identical, determinant = 0
- Interchanging two rows (or columns) changes sign of determinant
- If one row (or column) is multiple of another, determinant = 0
3
Area of Triangle Using Determinants
- Area formula uses coordinates of three vertices
- Always take absolute value for area (positive quantity)
- If area = 0, points are collinear
4
Minors and Cofactors
- Minor Mᵢⱼ = determinant after removing ith row and jth column
- Cofactor Cᵢⱼ = (-1)^(i+j) × Mᵢⱼ
- Sign pattern alternates in checkerboard fashion
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Key Concepts
For matrix A = [a₁₁ a₁₂Calculated using expansion along any rowFor triangle with vertices (x₁Minor Mᵢⱼ is determinant after removingAdjoint of matrix A is transpose
Frequently Asked Questions
What topics are covered in Determinants for KEAM?
Determinants is an important chapter in KEAM Mathematics. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: Introduction to Determinants, Properties of Determinants, Area of Triangle Using Determinants, Minors and Cofactors.
How important is Determinants for KEAM?
Determinants is a frequently tested chapter in KEAM Mathematics. Questions from this chapter appear regularly in previous year papers. There are 362 practice questions available for this chapter.
How to prepare Determinants for KEAM?
Start by understanding the core concepts, then solve practice questions. Focus on formulas and their applications. Use revision notes for quick review before the exam.
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