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.
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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
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
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
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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Sources & Official References
- Kerala Board of Public Examinations — keralapareekshabhavan.in
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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