Class 10 Maths Chapter 3 Exercise 3.2 Solutions 2026 – Matrices and Determinants Notes PDF

Unit 3: Matrices and Determinants | Exercise 3.2 | Punjab Board New Syllabus 2026–27

Updated August 2026: Exercise 3.2 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.

Doing Arithmetic on a Whole Grid at Once

Now that Exercise 3.1 has established what a matrix is and how to describe its order, Exercise 3.2 asks the natural next question: can two matrices be added together, or multiplied by an ordinary number? The answer is yes, and the rules are simpler than they might sound — every operation here works one entry at a time, matching positions exactly.

Key Concepts Covered in Exercise 3.2

Addition of Matrices

Two matrices can be added only if they have the exact same order. Addition is done entry by entry: the element in row i, column j of the sum is simply the sum of the elements in row i, column j of each matrix.

Subtraction of Matrices

Subtraction works exactly like addition — same order required, and each entry is subtracted from its corresponding entry in the other matrix.

Scalar Multiplication

Multiplying a matrix by a scalar (an ordinary number) means multiplying every single entry in the matrix by that number. Unlike addition, scalar multiplication works on a matrix of any order, since there’s no second matrix to match against.

Combining Operations

Many questions in this exercise combine addition, subtraction, and scalar multiplication in a single expression, such as 2A − 3B, requiring the scalar multiplication to be done first before adding or subtracting.

Step-by-Step Solved Examples

Q. No. 1: If A = [[2, 3], [1, 4]] and B = [[5, 0], [2, 1]], find A + B.

Add corresponding entries:

Position (1,1): 2+5=7   Position (1,2): 3+0=3

Position (2,1): 1+2=3   Position (2,2): 4+1=5

A + B = [[7, 3], [3, 5]]

Q. No. 2: If A = [[6, 4], [8, 2]], find 3A.

Multiply every entry by 3:

3A = [[3×6, 3×4], [3×8, 3×2]]

3A = [[18, 12], [24, 6]]

Q. No. 3: If A = [[4, 1], [3, 2]] and B = [[1, 2], [0, 3]], find 2A − B.

First find 2A: 2A = [[8, 2], [6, 4]]

Now subtract B: 2A − B = [[8−1, 2−2], [6−0, 4−3]]

2A − B = [[7, 0], [6, 1]]

These three questions are representative samples. The full PDF notes uploaded on this page walk through every question of Exercise 3.2 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 whether two given matrices can be added, based on their order
• Short Questions: Direct addition or subtraction of two matrices of the same order
• Long Questions: Combined expressions like 2A − 3B, requiring scalar multiplication before subtraction

Where This Matters Beyond This Exercise

Addition and scalar multiplication are the simplest matrix operations, but they set up the pattern of “match positions, then combine” that carries through to matrix multiplication in the next exercise — even though multiplication itself works differently. Outside the classroom, adding matrices is how image editing software blends two images, and scalar multiplication is how brightness or contrast is adjusted uniformly across an image.

Common Mistakes Students Make in Exercise 3.2

• Attempting to add two matrices of different orders, which is simply undefined
• Forgetting to multiply every single entry when performing scalar multiplication, not just some of them
• Losing track of signs when subtracting negative entries
• Doing addition/subtraction before completing the scalar multiplication in a combined expression

Why This Exercise Matters for the Board Exam

These operations are quick, mechanical, and low-risk once the order-matching rule is understood, making Exercise 3.2 a dependable source of marks in the short-question section. Combined expressions like 2A − 3B are a common long-question style, since they test both scalar multiplication and subtraction in one question.

Quick Links – Chapter 3: Matrices and Determinants

Links for sections other than Exercise 3.2 will be activated as they are published on this site.

Download Exercise 3.2 Notes PDF

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Frequently Asked Questions (FAQs)

Q1. Are these Exercise 3.2 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. Can any two matrices be added together?

No — matrices can only be added or subtracted if they have exactly the same order (same number of rows and columns). Scalar multiplication, however, works on a matrix of any order.

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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