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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.

45 questions20 flashcards5 concepts

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Key Topics to Revise

1

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
2

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
3

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)
4

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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Full Notes

Key Concepts

A determinant is a square arrangementTwo main methodsSeven key propertiesFor system a₁x + b₁y +For triangle with vertices A(x₁

Frequently Asked Questions

What are the important topics in Determinants for Maharashtra Board Class 11 Mathematics & Statistics?
Determinants covers several key topics that are frequently asked in Maharashtra Board Class 11 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Determinants — Maharashtra Board Class 11 Mathematics & Statistics?
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.

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