Class 10 Maths Chapter 3 Exercise 3.1 Solutions 2026 – Matrices and Determinants Notes PDF

Unit 3: Matrices and Determinants | Exercise 3.1 | Punjab Board New Syllabus 2026–27

Updated August 2026: Exercise 3.1 solutions for Matrices and Determinants have been uploaded below and are free to view or download, fully solved according to the new PCTB/PECTAA Class 10 Mathematics syllabus.

Organizing Numbers into a Grid

So far, numbers in this course have appeared one at a time or as coefficients inside an equation. A matrix takes a different approach entirely: it organizes many numbers into a neat grid of rows and columns, treating the whole grid as a single mathematical object. Exercise 3.1 introduces this idea from scratch — what a matrix is, how to describe its size, and how to recognize its most common types.

Key Concepts Covered in Exercise 3.1

What Is a Matrix

A matrix is a rectangular arrangement of numbers (called elements or entries) organized into rows and columns, usually enclosed in square brackets and named with a capital letter, like A or B.

Order of a Matrix

The order (or size) of a matrix is written as m × n, where m is the number of rows and n is the number of columns. A matrix with 2 rows and 3 columns has order 2 × 3 — always rows first, then columns.

Types of Matrices

This exercise introduces several special matrix types: a row matrix (only 1 row), a column matrix (only 1 column), a square matrix (equal rows and columns), a null or zero matrix (every entry is 0), and an identity matrix (a square matrix with 1s on the main diagonal and 0s everywhere else).

Equality of Matrices

Two matrices are equal only when they have exactly the same order and every corresponding entry matches. A 2×3 matrix can never equal a 3×2 matrix, even if they contain the same numbers, because their orders differ.

Step-by-Step Solved Examples

Q. No. 1: State the order of the matrix A = [[2, 5, 1], [0, 4, 7]].

Count the rows: 2

Count the columns: 3

Order of A = 2 × 3

Q. No. 2: Identify the type of the matrix B = [[1, 0], [0, 1]].

B has 2 rows and 2 columns, so it is a square matrix.

The diagonal entries are both 1, and the off-diagonal entries are both 0.

This makes B an identity matrix, specifically the 2×2 identity matrix I₂.

Q. No. 3: Find the values of x and y if [[x, 3], [4, y]] = [[7, 3], [4, 9]].

Since the matrices are equal, corresponding entries must match:

Position (1,1): x = 7

Position (2,2): y = 9

So x = 7 and y = 9

These three questions are representative samples. The full PDF notes uploaded on this page walk through every question of Exercise 3.1 in the same numbered, step-by-step format.

MCQs, Short Questions & Long Questions from This Exercise

Alongside the main exercise, this page’s uploaded notes are organized the way Punjab Board papers are structured, so students can practice by question type:

• MCQs: Quick questions on stating a matrix’s order or identifying its type
• Short Questions: Identifying row, column, square, null, and identity matrices from given examples
• Long Questions: Solving for unknown variables using the equality of matrices

Where This Matters Beyond This Exercise

Everything in the rest of this chapter — addition, multiplication, determinants, and inverses — depends on first knowing a matrix’s order and type, since many operations (like addition) are only defined between matrices of matching order. Outside the classroom, matrices are the standard way computers store and transform data in graphics, statistics, and machine learning.

Common Mistakes Students Make in Exercise 3.1

• Writing the order as columns × rows instead of rows × columns
• Confusing a square matrix (equal rows and columns) with an identity matrix (which must also have 1s on the diagonal)
• Assuming two matrices with the same entries in a different arrangement are equal
• Miscounting rows or columns in a larger matrix

Why This Exercise Matters for the Board Exam

Exercise 3.1 is largely definitional, which makes it a fast, low-risk source of marks in the objective and short-question sections — as long as the vocabulary (order, row/column/square/null/identity matrix) is memorized precisely. A shaky grasp of these basic terms often causes avoidable mistakes throughout the rest of the chapter, so it’s worth mastering thoroughly here.

Quick Links – Chapter 3: Matrices and Determinants

Links for sections other than Exercise 3.1 will be activated as they are published on this site.

Download Exercise 3.1 Notes PDF

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Frequently Asked Questions (FAQs)

Q1. Are these Exercise 3.1 notes free to download?

Yes, all notes on this page are completely free to view and download in PDF format.

Q2. Which board are these notes for?

These notes are prepared according to the Punjab Board syllabus and are useful for all Punjab boards (Lahore, Gujranwala, Multan, Sargodha, Rawalpindi, Faisalabad, DG Khan, Bahawalpur, Sahiwal) as well as the Federal Board (FBISE).

Q3. Do I need to know earlier chapters before starting Exercise 3.1?

No — Chapter 3 (Matrices and Determinants) is independent of Chapters 1 and 2. Exercise 3.1 introduces matrices completely from scratch.

Q4. Does this page include MCQs and short questions too?

Yes, the uploaded notes include MCQs, short questions, and long questions related to this exercise’s topics, organized by question type to match the board paper pattern.

Q5. How can I download the PDF?

Click the “Download PDF” button above and the notes will open or download directly to your device.

Q6. Are these notes updated for the new 2026–27 syllabus?

Yes, these notes are prepared strictly according to the latest PCTB/PECTAA syllabus for the 2026–27 academic session.

Comments & Feedback

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