Business Mathematics and Basic Statistics · Ch 10 — Matrices (up to 2×2)

Matrix Notation, Order, Rows and Columns

This WBCHSE Class 12 Commerce Business Mathematics and Basic Statistics chapter introduces matrices — a compact way of arranging numbers in rows and columns that businesses use every day to organise data such as sales figures, stock levels, or prices across products and branches.

What is a matrix?

A matrix is a rectangular arrangement of numbers, set out in rows (horizontal lines) and columns (vertical lines), enclosed in brackets. For example, a shop tracking the number of two products, Pen and Pencil, sold on two consecutive days could record its sales as

A = \begin{pmatrix} 12 & 8 \\ 15 & 10 \end{pmatrix}

where the first row is Day 1's sales and the second row is Day 2's sales; the first column is Pen and the second column is Pencil.

Order of a matrix

If a matrix has $m$ rows and $n$ columns, it is said to be of order $m \times n$ (read " $m$ by $n$ "), rows always named first, then columns. The matrix $A$ above has 2 rows and 2 columns, so it is of order $2\times2$ . This chapter works only with matrices up to order $2\times2$ — the smallest square arrangement, and the one most commonly used in introductory commerce mathematics.

Elements of a matrix

Each individual number inside a matrix is called an element, written $a_{ij}$ , where $i$ is the row number and $j$ is the column number of that element (again, row before column). In the matrix $A$ above, $a_{11}=12$ (row 1, column 1), $a_{12}=8$ (row 1, column 2), $a_{21}=15$ , and $a_{22}=10$ .

Note

Row first, always

Both the order of a matrix ( $m\times n$ ) and the subscript of an element ( $a_{ij}$ ) always name the ROW before the COLUMN. Reversing this is the single most common notation slip students make with matrices.

The general form of a $2\times2$ matrix — the only order this chapter uses — is written

A = \begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix}

Matrices of this kind are a standard tool across commerce-mathematics curricula nationally for organising and manipulating tabular business data, applied here to WBCHSE's own Class 12 Business Mathematics and Basic Statistics syllabus.

Definition 1Matrix

A rectangular arrangement of numbers in rows and columns, enclosed in brackets. This chapter works only with matrices up to order 2×2.

Definition 2Order of a Matrix

If a matrix has m rows and n columns, its order is written m × n — rows always named first, then columns.

Definition 3Element a_{ij}

The number occupying the i-th row and j-th column of a matrix, written $a_{ij}$ — the row subscript is always written first.

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