Exercise 3.3 Class 10 Math Solutions – Matrix Operations & Addition Laws, Punjab Board

Solved Exercise 3.3 for Class 10 Mathematics, Punjab Board. Detailed step-by-step notes covering algebraic operations on matrices: scalar multiplication, matrix addition, subtraction, commutative and associative laws, additive identity, and additive inverse of matrices.

This page provides complete solved solutions for Exercise 3.3 from Unit 3: Matrices and Determinants, Class 10 Mathematics, Punjab Board (PCTB). It covers algebraic operations on matrices including scalar multiplication (k A), matrix addition and subtraction (A ± B when orders are identical), verification of commutative and associative laws of addition (A + B = B + A and (A + B) + C = A + (B + C)), additive identity (O), and additive inverse (-A). All questions are worked out step by step for Matric Part 2 students.
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Exercise Overview

Exercise 3.3 is the algebraic core of Unit 3: Matrices and Determinants in Class 10 Punjab Board Mathematics. Building on matrix definitions and types from preceding sections, this exercise develops students' computational mastery in executing fundamental matrix arithmetic operations and proving formal algebraic laws.

The exercise begins with conformability criteria: two matrices can only be added or subtracted if they share identical orders (m × n), adding or subtracting corresponding entries. Students also practice scalar multiplication by scaling every element of a matrix by a real constant k. Beyond standard computation, the exercise rigorously tests the algebraic properties of matrix addition, including the verification of the Commutative Law (A + B = B + A) and the Associative Law ((A + B) + C = A + (B + C)). Additionally, students determine the additive identity (the zero matrix O) and calculate the additive inverse (-A) by negating all matrix entries to satisfy A + (-A) = O.

In Punjab Board examinations (including Lahore, Faisalabad, Rawalpindi, Gujranwala, Multan, and other BISE boards), Exercise 3.3 problems are frequently selected for Section B (Short Questions) and multi-part sub-questions in Section C. Mastering these step-by-step matrix addition, subtraction, and property verification proofs guarantees precision and full marks on board test papers.

FAQs

Are these Exercise 3.3 solutions according to the Punjab Board syllabus?
Yes. These solutions follow the Punjab Curriculum and Textbook Board (PCTB) syllabus for Class 10 Mathematics, covering all Unit 3 Exercise 3.3 operations and laws for the 2026-2027 session.
What is the condition for addition and subtraction of matrices?
Two matrices A and B can be added or subtracted if and only if they are conformable, meaning they have the exact same order (same number of rows and columns).
How is scalar multiplication of a matrix performed?
To multiply a matrix A by a real scalar number k, multiply every individual entry of matrix A by k, resulting in kA.
Does matrix addition obey the commutative law?
Yes. For any two matrices A and B of the same order, A + B = B + A, proving that matrix addition is commutative.
What is the associative law of matrix addition?
For any three matrices A, B, and C of the same order, (A + B) + C = A + (B + C), showing that matrix addition is associative.
What is the additive identity of a matrix in Exercise 3.3?
The additive identity of a matrix A of order m × n is the zero matrix O of the same order, such that A + O = O + A = A.
How do you find the additive inverse of a matrix?
The additive inverse of a matrix A is -A, obtained by changing the sign of every entry in A, such that A + (-A) = (-A) + A = O (the zero matrix).
Can students read these Exercise 3.3 solutions online?
Yes, the complete solved PDF notes for Exercise 3.3 are embedded to read online directly on MaryamNotes.pk with no compulsory download.
Are these Exercise 3.3 solutions free for students?
Yes, all Exercise 3.3 solutions on MaryamNotes.pk are 100% free to read online for all Class 10 students across all Punjab boards.