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Formula Sheet

Applications of Matrices and Determinants

ICSE · Class 12 · Mathematics

All formulas from Applications of Matrices and Determinants in ICSE Class 12 Mathematics. Key equations, constants, and identities for board exam preparation.

101 questions28 flashcards5 concepts

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An illustration showing a triangle with its vertices labeled, alongside the determinant formula used to calculate its area.
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13 Formulas · 4 Sections

Formulas

1. Core Matrix Form and Basic Definitions

AX=B

A=[[a1,b1,c1],[a2,b2,c2],[a3,b3,c3]], X=[x,y,z]^T, B=[d1,d2,d3]^T

2. Consistency, Inconsistency, and Homogeneous Systems

If |A|≠0, then X=A^-1B

A^-1=(1/|A|)(adj A)

If |A|=0: inconsistent if (adj A)B≠O; consistent and dependent if (adj A)B=O

For A^T X=B, X=(A^T)^-1B=(A^-1)^T B

3. Matrix Method / Martin's Rule

X=A^-1B

A^-1=(1/|A|)(adj A)

If AB=kI, then A^-1=(1/k)B

4. Determinants in Coordinate Geometry

Δ=(1/2)|[x1 y1 1; x2 y2 1; x3 y3 1]|=(1/2)[x1(y2-y3)-y1(x2-x3)+(x2y3-x3y2)]

Area of triangle = |Δ|

Points A, B, C are collinear if Δ=0

Equation of line through (x1,y1) and (x2,y2): |[x y 1; x1 y1 1; x2 y2 1]|=0

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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 Decision Tree for Determining System Consistency, Complete Overview of Matrices and Determinants Applications, Mind map showing the three main branches of the chapter: consistency analysis, matrix solving methods, and coordinate geometry applications. These are the concepts ICSE Class 12 examiners draw on most — study them first, then practise related questions.
How to score full marks in Applications of Matrices and Determinants — ICSE Class 12 Mathematics?
Understand the core concepts first, then work through the 101 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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