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Important Questions

Applications of Matrices and Determinants

ICSE · Class 12 · Mathematics

Most important questions from Applications of Matrices and Determinants for ICSE Class 12 Mathematics board exam 2026. MCQs, short answer, and long answer questions with marks.

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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101 Questions·
multiple choicetrue false

Sample Questions

1multiple choice
1 marks

A system AX = O (where O is the zero matrix) is called:

Show answer

Homogeneous

A system is homogeneous when all constant terms are zero, i.e., B = O.

2true false
1 marks

A homogeneous system AX = O is always consistent.

Show answer

True

X = O (trivial solution) always satisfies AX=O. So a homogeneous system always has at least one solution and is therefore always consistent.

3multiple choice
1 marks

The formula for A⁻¹ in terms of adj A is:

Show answer

A⁻¹ = adj A / |A|

A⁻¹ = (adj A)/|A|. This requires |A| ≠ 0.

4multiple choice
1 marks

If C_ij is the cofactor of element a_ij, then the cofactor C_ij equals:

Show answer

(−1)^(i+j) × M_ij

Cofactor = (−1)^(i+j) × minor. The sign alternates in a checkerboard pattern.

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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.
How many important questions are there in Applications of Matrices and Determinants?
There are 101 practice questions available for Applications of Matrices and Determinants. These cover multiple question types including MCQs, short answer, and long answer questions.

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Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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