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Revision Notes

Determinants and their Applications

Kerala Board · Class 12 · Mathematics

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

45 questions20 flashcards5 concepts

Key Topics to Revise

1

Determinant of Order 2

  • For a 2×2 matrix A = [a₁₁ a₁₂; a₂₁ a₂₂], |A| = a₁₁a₂₂ - a₁₂a₂₁
  • Use the diagonal method: multiply main diagonal elements and subtract product of anti-diagonal elements
  • Always calculate step-by-step to avoid sign errors
2

Determinant of Order 3

  • Can be expanded along any row or column using cofactors
  • Sarrus diagram method provides quick calculation for 3×3 determinants
  • Sign pattern follows (-1)^(i+j) where i is row number and j is column number
3

Properties of Determinants

  • Determinant value remains same when rows and columns are interchanged
  • Swapping two rows/columns changes sign of determinant
  • If any row/column has all zeros, determinant = 0
4

System of Linear Equations - Cramer's Rule

  • Applicable only when D ≠ 0 (coefficient determinant is non-zero)
  • For 2 variables: x = D₁/D, y = D₂/D
  • For 3 variables: x = D₁/D, y = D₂/D, z = D₃/D

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Full Notes

Key Concepts

For a 2×2 matrix A =For a 3×3 matrixMinor Mᵢⱼ of element aᵢⱼAlternative method for 3×3 determinantsKey properties include

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Frequently Asked Questions

What are the important topics in Determinants and their Applications for Kerala Board Class 12 Mathematics?

Determinants and their Applications covers several key topics that are frequently asked in Kerala Board Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.

Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision before the exam.

Sources & Official References

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