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

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

Updated August 2026: Review Exercise 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.

Testing the Whole Chapter at Once

Each exercise in this chapter built one skill at a time — order and types, then arithmetic, then multiplication, then determinants, inverses, and finally solving equations. The Review Exercise removes those labels and mixes everything together, the way a real board paper naturally combines two or three matrix skills inside a single question.

What This Review Exercise Draws On

Matrix Basics and Equality

Quick-recall questions on order, matrix types, and equality of matrices, exactly as introduced in Exercise 3.1.

Operations in Combination

Problems that chain addition, scalar multiplication, and full matrix multiplication together within a single expression.

Determinants and Inverses

Mixed questions calculating a determinant, checking whether a matrix is singular, and finding an inverse where one exists.

Solving Systems of Equations

Full applications of the X = A⁻¹B method from Exercise 3.6, sometimes requiring the determinant and inverse to be calculated first as part of the same question.

Step-by-Step Solved Examples

Q. No. 1: If A = [[2, 1], [0, 3]] and B = [[1, 4], [2, 1]], find |AB| without fully computing AB first.

Property used: |AB| = |A| × |B|

|A| = (2×3) − (1×0) = 6

|B| = (1×1) − (4×2) = 1 − 8 = −7

|AB| = 6 × (−7) = −42

Q. No. 2: Find the inverse of A = [[5, 3], [2, 1]] and use it to solve 5x + 3y = 11, 2x + y = 4.

|A| = (5×1) − (3×2) = 5 − 6 = −1

adj A = [[1, −3], [−2, 5]]

A⁻¹ = (1/−1)[[1, −3], [−2, 5]] = [[−1, 3], [2, −5]]

X = A⁻¹B = [[−1, 3], [2, −5]] × [[11], [4]]

x = (−1×11)+(3×4) = −11+12 = 1

y = (2×11)+(−5×4) = 22−20 = 2

Solution: x = 1, y = 2

Q. No. 3: State whether the matrix [[3, 6], [1, 2]] is singular, and explain what this means for solving equations with it.

|A| = (3×2) − (6×1) = 6 − 6 = 0

Since |A| = 0, the matrix is singular and has no inverse.

This means the matrix method (X = A⁻¹B) cannot be used to find a unique solution for any system with this coefficient matrix.

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

MCQs, Short Questions & Long Questions from This Review

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: Rapid-fire recall across all six exercises, useful for timed practice
• Short Questions: Two-step problems combining any two of the chapter’s core ideas
• Long Questions: Full multi-part problems that mirror the structure of an actual board exam question

Study Tips for Reviewing This Chapter

• Attempt the Review Exercise only after completing Exercises 3.1 through 3.6
• Keep the four key formulas — determinant (ad−bc), adjoint, inverse, and X=A⁻¹B — written together on one page for quick reference while revising
• Practice the |AB| = |A|×|B| shortcut, since it saves significant time on mixed questions like Q. No. 1
• Re-attempt any question you got wrong the next day, rather than only reading the correct answer once

Common Mistakes Students Make in This Review Exercise

• Trying to answer a multi-step question in one line instead of solving it stage by stage
• Applying a rule from the wrong exercise — for example, adding matrices of different orders
• Forgetting to check |A| ≠ 0 before attempting to find an inverse or solve a system

Why This Exercise Matters for the Board Exam

Board papers rarely test a single matrix skill in isolation, which is exactly what this Review Exercise simulates. Working through it carefully is one of the best ways to confirm genuine readiness for Chapter 3 before moving on to Chapter 4.

Quick Links – Chapter 3: Matrices and Determinants

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

Download Review Exercise Notes PDF

Click below to view or download the complete Review Exercise notes in PDF format.

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Frequently Asked Questions (FAQs)

Q1. Are these Review Exercise 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. When should I attempt the Review Exercise?

Only after completing all six exercises (3.1 to 3.6), since the questions here mix topics from across the chapter without labeling which exercise each one came from.

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

Yes, the uploaded notes include MCQs, short questions, and long questions covering the whole chapter, 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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