Determinants Class 12 Maths Notes – Formulas & Quick Revision

Determinants mein expansion, adjoint, inverse aur linear equations ka matrix method aata hai. Yahan aapko is chapter ke sabse important formulas aur quick revision points free milte hain — NCERT/CBSE syllabus ke hisaab se, boards aur JEE/NEET dono ke liye.

Important Formulas & Concepts — Determinants

• 2×2: |A| = ad − bc
• Adjoint: adj(A) = cofactor matrix ka transpose
• A⁻¹ = adj(A)/|A|
• |adj A| = |A|ⁿ⁻¹
• |AB| = |A||B|; |kA| = kⁿ|A|
• Area of triangle = ½|x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)|
• AX = B → X = A⁻¹B
• Consistent: |A| ≠ 0 unique solution; |A| = 0 check (adj A)B

Quick Revision Points

• Cofactor mein sign (−1)^(i+j) mat bhoolo
• Row/column same ho to determinant zero
• Matrix method ka 6-marker boards mein almost pakka hai
• |A| = 0 aur (adj A)B ≠ 0 → inconsistent
• Determinant scalar hota hai, matrix nahi

FAQ

Matrix method ka question kaisa hota hai?

3 equations ko AX = B mein likho, A⁻¹ nikalo, X = A⁻¹B — PDF mein full solved format hai.

Properties se simplification aati hai?

Rationalised syllabus mein properties kam hain — expansion aur inverse par focus karo.

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