Determinants
Maharashtra Board · Class 11 · Mathematics & Statistics
Quick revision notes for Determinants — Maharashtra Board Class 11 Mathematics & Statistics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Definition and Basic Concepts
- A determinant of order 2 is |a b|/|c d| = ad - bc
- A determinant of order 3 has 9 elements arranged in 3 rows and 3 columns
- Element aᵢⱼ represents the element in ith row and jth column
Properties of Determinants
- Property 1: Determinant remains unchanged when rows and columns are interchanged (transpose)
- Property 2: Interchanging any two rows or columns changes the sign of the determinant
- Property 3: If any two rows or columns are identical, the determinant equals zero
Problem-Solving Techniques and Methods
- Method 1: Direct expansion along any row or column (preferably with most zeros)
- Method 2: Using properties to create zeros and simplify before expansion
- Method 3: Sarrus rule for 3×3 determinants (diagonal method)
Cramer's Rule
- Used to solve systems of linear equations in three variables
- System: a₁x + b₁y + c₁z = d₁, a₂x + b₂y + c₂z = d₂, a₃x + b₃y + c₃z = d₃
- Solutions: x = Dₓ/D, y = Dᵧ/D, z = Dᵤ/D (provided D ≠ 0)
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