Skip to main content
Super TutorResources
Chapter 7 of 13
Concept Maps

Applications of Matrices and Determinants — Concept Maps

ICSE · Class 12 · Mathematics

4 concept maps of Applications of Matrices and Determinants for ICSE Class 12 Mathematics, each also written out as a text outline.

101 questions28 flashcards14 formulas & key relations5 concepts

Interactive on Super Tutor

Studying Applications of Matrices and Determinants? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for concept maps and more.

Try Super Tutor — Free

Free trial, no card needed.

An illustration showing a triangle with its vertices labeled, alongside the determinant formula used to calculate its area.
Super Tutor

One of 2 illustrations for Applications of Matrices and Determinants in Super Tutor — alongside flashcards, concept maps and practice questions.

4 Concept Maps

Decision Tree for Determining System Consistency

Decision Tree for Determining System Consistency

The map in words

  • System of Linear Equations
    • Homogeneous AX = O?
      • Yes: Always Consistent
        • Calculate |A|
          • A ≠ 0: Unique Solution Only x=0, y=0, z=0 Trivial Solution
          • A = 0: Infinitely Many Solutions Non-trivial Solutions
      • No: Non-Homogeneous AX = B
        • Calculate |A|
          • A ≠ 0: Consistent & Independent Unique Solution
          • A = 0: Is adjA·B = 0?
            • Yes: Consistent & Dependent Infinitely Many
            • No: Inconsistent No Solution

Complete Overview of Matrices and Determinants Applications

Complete Overview of Matrices and Determinants Applications

The map in words

  • Applications of Matrices and Determinants
    • Consistency Analysis
      • Non-Homogeneous Systems
        • |A| ≠ 0
          • Unique Solution
        • |A| = 0
          • Check adj(A)B
            • adj(A)B = O
              • Infinitely Many
            • adj(A)B ≠ O
              • Inconsistent
      • Homogeneous Systems
        • Always Consistent
        • |A| ≠ 0
          • Trivial Only
        • |A| = 0
          • Infinitely Many
    • Matrix Method
      • Finding A inverse
        • Calculate |A|
        • Find Cofactors
        • Get Adjoint
        • A⁻¹ = (1/|A|)adj(A)
      • Solution Formula
        • X = A⁻¹B
        • 2×2 Quick Formula
        • 3×3 Using Cofactors
    • Coordinate Geometry
      • Triangle Area
        • Using Determinant
        • Signed vs Absolute
      • Collinearity
        • Three Points
        • Determinant = 0
      • Line Equations
        • From Two Points
        • Determinant Form

Mind map showing the three main branches of the chapter: consistency analysis, matrix solving methods, and coordinate geometry applications

Mind map showing the three main branches of the chapter: consistency analysis, matrix solving methods, and coordinate geometry applications

The map in words

  • Applications of Matrices and Determinants
    • Consistency of Systems
      • Non-Homogeneous
        • Two Variables
        • Three Variables
      • Homogeneous Systems
        • Trivial Solution
        • Non-trivial Solution
    • Matrix Method
      • Finding Inverse
      • Solving AX=B
      • Applications
    • Coordinate Geometry
      • Area of Triangle
      • Collinearity
      • Equation of Line

Applications of matrices and determinants in solving linear systems and coordinate geometry

Applications of matrices and determinants in solving linear systems and coordinate geometry

The map in words

  • Applications of matrices and determinants in solving linear systems and coordinate geometry
    • Matrix form of a linear system
    • Consistency of a system
    • Homogeneous and non-homogeneous systems
    • Matrix Method or Martin's Rule
    • Consistency test using determinant and adjoint
    • Adjoint and inverse of a matrix
    • Transpose system
    • Coordinate geometry applications of determinants

Explore these maps interactively

Explore Diagrams

Frequently Asked Questions

What are the important topics in Applications of Matrices and Determinants for ICSE Class 12 Mathematics?
Key topics in Applications of Matrices and Determinants include System of Linear Equations in Matrix Form, Consistency and Inconsistency Tests, Matrix Method and Inverse of a Matrix, Coordinate Geometry Applications of Determinants. Study these first, then practise questions on each for the ICSE Class 12 board exam.
What do the concept maps for Applications of Matrices and Determinants show?
The 4 maps show how the ideas in Applications of Matrices and Determinants connect: Decision Tree for Determining System Consistency; Complete Overview of Matrices and Determinants Applications. Each map is also written out as an outline on this page.
How should I revise Applications of Matrices and Determinants for the ICSE Class 12 board exam?
Learn the core ideas first, then work through the 101 practice questions on Applications of Matrices and Determinants. Revise 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.

More resources for Applications of Matrices and Determinants

All ICSE Class 12 Mathematics Concept Maps

For serious students

Get the full Applications of Matrices and Determinants chapter — start free.

Quizzes, flashcards, an AI doubt solver and a study plan for ICSE Class 12 Mathematics. Free to start, no card needed.

Try Super Tutor Free
Try this chapter free