Determinants
Karnataka Board · Class 12 · Mathematics
Quick revision notes for Determinants — Karnataka Board Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
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Basic Concepts and Definitions
- Determinants are only defined for square matrices
- A determinant is a function that associates each square matrix with a unique number
- Determinants are denoted by |A|, det A, or Δ
3×3 Determinants and Expansion
- 3×3 determinants can be expanded along any row or column
- All expansions give the same result
- Choose row/column with maximum zeros for easier calculation
Properties of Determinants
- If any row or column has all zeros, determinant = 0
- Interchanging two rows/columns changes sign of determinant
- If two rows/columns are identical, determinant = 0
Area of Triangle Using Determinants
- Area formula uses coordinates of three vertices
- Result is always taken as absolute value
- If area = 0, the three points are collinear
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Sources & Official References
- Karnataka SSLC — kseeb.kar.nic.in
- Dept of Pre-University Education, Karnataka
- 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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