2.1 Q-1

Exercise 2.1 — Question 1

Objective

Identify the order of a matrix and classify matrices by type.

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Key Concepts

Order of a Matrix

A matrix with $m$ rows and $n$ columns has order $m\times n$.

$A=[a_{ij}{]}_{m\times n}$

where $i=1,2,\dots ,m$ and $j=1,2,\dots ,n$.

Types of Matrices

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Worked Examples

Example 1. State the order of each matrix and classify it.

$A=\left[\begin{array}{ccc}3& -1& 2\end{array}\right]$

Solution: $A$ has 1 row and 3 columns → order $1\times 3$ → Row matrix.

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$B=\left[\begin{array}{c}5\\ -2\\ 7\end{array}\right]$

Solution: $B$ has 3 rows and 1 column → order $3\times 1$ → Column matrix.

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$C=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

Solution: $C$ has 2 rows and 2 columns, $m=n=2$ → order $2\times 2$ → Square matrix.

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$D=\left[\begin{array}{ccc}2& 4& 6\\ 1& 3& 5\end{array}\right]$

Solution: $D$ has 2 rows and 3 columns, $m\ne n$ → order $2\times 3$ → Rectangular matrix.

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Quick Rule