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Syllabus

Matrices — Syllabus

Punjab Board · Class 12 · Mathematics

What Matrices covers in Punjab Board Class 12 Mathematics: 4 topics, for the 2026-27 session. Part of the Punjab Board Class 12 Mathematics syllabus.

45 questions25 flashcards3 formulas & key relations5 concepts

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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.
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4 Topics · Punjab Board Class 12 Mathematics · 2026-27

Topics in Matrices

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.

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

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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.

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All Punjab Board Class 12 Mathematics Syllabus

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