Skip to main content
Super TutorResources
Chapter 4 of 5
QuestionsNotesFlashcardsSummaryFormulasQuizConceptsSyllabusPlan
Revision Notes

Determinants

Punjab Board · Class 12 · Mathematics

Quick revision notes for Determinants — Punjab Board Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

44 questions25 flashcards5 concepts

Interactive on Super Tutor

Studying Determinants? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for revision notes and more.

Try Super Tutor — Free

1,000+ Class 12 students started this chapter today

A visual representation defining a determinant as a scalar value associated with a square matrix, showing its notation and basic structure.
Super Tutor

This is just one of 11+ visuals inside Super Tutor's Determinants chapter

Explore the full set

Key Topics to Revise

1

Introduction to Determinants

  • Every square matrix A = [aij] of order n has an associated number called its determinant, denoted by |A|, det(A), or Δ
  • Only square matrices have determinants — rectangular matrices do NOT have determinants
  • |A| is read as 'determinant of A', NOT 'modulus of A'
2

Expansion of Determinants (3×3 Order)

  • A 3×3 determinant can be expanded along ANY row or column — the value remains the SAME
  • There are 6 ways to expand a 3×3 determinant: along R1, R2, R3, C1, C2, C3
  • Sign pattern for cofactor expansion: (-1)^(i+j) — forms a checkerboard of + and - signs
3

Minors and Cofactors

  • Minor Mij is the determinant of the matrix obtained by deleting the ith row and jth column
  • Cofactor Aij = (-1)^(i+j) × Mij — cofactor is minor with appropriate sign
  • If (i+j) is EVEN, cofactor = +Minor; if (i+j) is ODD, cofactor = -Minor
4

Area of a Triangle Using Determinants

  • Area of triangle with vertices (x1,y1), (x2,y2), (x3,y3) can be expressed as a determinant
  • Area Δ = (1/2)|det| where det is the 3×3 determinant with the coordinates
  • Area is ALWAYS positive — take the absolute value of the determinant

Get complete notes with diagrams and examples

Full Notes

Key Concepts

A determinant is a realFor a matrix A = [a]For a 2×2 matrix [[a₁₁For a 3×3 matrixThe minor M_ij of element a_ij

Frequently Asked Questions

What are the important topics in Determinants for Punjab Board Class 12 Mathematics?
Key topics in Determinants include Determinants - Complete Chapter Overview, Determinants - Complete Concept Map, Determinants – Complete Chapter Overview. These are the concepts Punjab Board Class 12 examiners draw on most — study them first, then practise related questions.
How to score full marks in Determinants — Punjab Board Class 12 Mathematics?
Understand the core concepts first, then work through the 44 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Determinants

All 5 chapters — Punjab Board Class 12 Mathematics Revision Notes

For serious students

Get the full Determinants chapter — for free.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan for Punjab Board Class 12 Mathematics.

Try Super Tutor Free
Try the full chapter — Free