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Determinants and their Applications

Telangana Open School (TOSS) · Class 12 · Mathematics

Quick revision notes for Determinants and their Applications — Telangana Open School (TOSS) Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

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Key Topics to Revise

1

Determinant of Order 2

  • A 2×2 determinant is calculated as the product of the main diagonal minus the product of the other diagonal.
  • The value of the determinant determines whether a system of two linear equations has a unique solution.
  • If the determinant is zero, the system either has no solution or infinitely many solutions.
2

Determinant of Order 3

  • Can be expanded using any row or column, but usually the first row is used.
  • Each element is multiplied by its cofactor (minor with proper sign).
  • The sign pattern follows a checkerboard: + - +, - + -, + - + starting from top-left.
3

Properties of Determinants

  • Interchanging two rows/columns changes the sign of the determinant.
  • If two rows/columns are identical or proportional, determinant is zero.
  • Multiplying a row/column by k multiplies the determinant by k.
4

Cramer's Rule and Applications

  • Cramer's Rule solves system of linear equations using determinants.
  • Only applicable when main determinant D ≠ 0.
  • For system ax+by=e, cx+dy=f: x = D₁/D, y = D₂/D where D₁ replaces x-column with constants, D₂ replaces y-column.

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Full Notes

Key Concepts

For a 2×2 matrix with elementsA 3×3 determinant can be expandedThe minor of an elementKey properties includeA method to solve a system

Frequently Asked Questions

What are the important topics in Determinants and their Applications for Telangana Open School (TOSS) Class 12 Mathematics?
Determinants and their Applications covers several key topics that are frequently asked in Telangana Open School (TOSS) Class 12 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 and their Applications — Telangana Open School (TOSS) Class 12 Mathematics?
Understand the core concepts first, then work through the 57 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall 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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