Lesson 1, Topic 1
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Introduction – Matrices (Matrix)

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What is a Matrix?

A matrix is a set of elements arranged in rows and columns to form a rectangular arrays.

A matrix having m rows and n columns is called m × n (i.e, ‘m by n’) matrix and is referred to as having order m × n.

A matrix is indicated by writing the array within brackets.

Example: $$\scriptsize \begin{pmatrix} 5 & 7 & 2 \\ 6 & 3 & 8 \end{pmatrix}$$

This is a 2 × 3 matrix, i.e. a ‘2 by 3’ matrix, 5, 7, 2, 6, 3, and 8 are elements of the matrix.

Note: In describing the matrix, the number of rows is stated first and the number of columns second.

$$\scriptsize \begin{pmatrix} 5 & 6 & 4 \\ 2 & -3 & 2\\ 7 & 8 & 7 \\ 6 & 7 & 5 \end{pmatrix}$$

This is a matrix of order 4 × 3, i.e. 4 rows and 3 columns. In general, a matrix of m × n denotes m rows and n columns.

Double Suffix Notation

Each element in a matrix has its own particulars address or location which can be defined by a system of double suffixes, the first indicating the row, the second the column.

$$\scriptsize \begin{pmatrix} a_{11} & a_{12} & a_{13} & a_{14} \\ a_{21} & a_{22} & a_{23} & a_{24}\\ a_{31} & a_{32} & a_{33} & a_{44} \end{pmatrix}$$

Therefore, a23 is indicating the element in the second row and third column.

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