Skip to main content
Super TutorResources
Chapter 3 of 5
Revision Notes

Matrices — Revision Notes

Punjab Board · Class 12 · Mathematics

Matrices revision notes for Punjab Board Class 12 Mathematics: 4 topics in quick points. Part of the Punjab Board Class 12 Mathematics syllabus.

45 questions25 flashcards3 formulas & key relations5 concepts

Interactive on Super Tutor

Studying Matrices? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for revision notes and more.

Try Super Tutor — Free

Free trial, no card needed.

A visual representation of a matrix, clearly showing its elements, rows, columns, and how its order (m x n) is defined. Highlight the 'a_ij' notation for elements.
Super Tutor

One of 11 illustrations for Matrices in Super Tutor — alongside flashcards, concept maps and practice questions.

Key Topics to Revise

1

Definition and Order of a Matrix

  • A matrix is an ordered rectangular array of numbers or functions enclosed in square brackets [ ].
  • The numbers or functions inside the matrix are called elements or entries.
  • Matrices are denoted by capital letters A, B, C, etc.
2

Types of Matrices

  • Column Matrix: Only one column (order m×1). Example: [2; -1; 3] is a 3×1 column matrix.
  • Row Matrix: Only one row (order 1×n). Example: [1, 2, -3, 4] is a 1×4 row matrix.
  • Square Matrix: Number of rows = Number of columns (order n×n). Example: A 3×3 matrix.
3

Operations on Matrices — Addition and Scalar Multiplication

  • ADDITION: Two matrices can be added ONLY if they have the same order.
  • If A = [a_ij] and B = [b_ij] are both m×n matrices, then A + B = [a_ij + b_ij]_{m×n} (add corresponding elements).
  • SCALAR MULTIPLICATION: kA = k[a_ij] = [ka_ij] — multiply every element by the scalar k.
4

Multiplication of Matrices

  • CONDITION FOR MULTIPLICATION: AB is defined ONLY IF the number of columns in A = number of rows in B.
  • If A is m×n and B is n×p, then AB is m×p (the inner dimensions n must match; the result takes outer dimensions m×p).
  • The (i,k)-th element of AB: c_ik = Σ(j=1 to n) a_ij × b_jk = a_i1×b_1k + a_i2×b_2k + ... + a_in×b_nk.

Get complete notes with diagrams and examples

Full Notes

Key Concepts

A matrix is an ordered rectangularMatrices can be classified into severalTwo matrices A and B canWhen a matrix A is multipliedFor matrices A (m×n) and B

Frequently Asked Questions

What are the important topics in Matrices for Punjab Board Class 12 Mathematics?
Key topics in Matrices include Definition and Order of a Matrix, Types of Matrices, Operations on Matrices — Addition and Scalar Multiplication, Multiplication of Matrices. Study these first, then practise questions on each for the Punjab Board Class 12 board exam.
How should I revise Matrices for the Punjab Board Class 12 board exam?
Learn the core ideas first, then work through the 45 practice questions on Matrices. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

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

More resources for Matrices

All Punjab Board Class 12 Mathematics Revision Notes

For serious students

Get the full Matrices chapter — start free.

Quizzes, flashcards, an AI doubt solver and a study plan for Punjab Board Class 12 Mathematics. Free to start, no card needed.

Try Super Tutor Free
Try this chapter free