Question

Order of a given matrix is m×1, m belongs to N ,What is the type of the given matrix?

Answer 1

Given :

Order of matrix is mx1.

m belongs to N,

To find :

Type of matrix.

Solution :

Order of matrix represents number of rows and columns in a matrix.

In the order of matrix m x n,

m represents number of rows in a matrix and

n represents number of columns in a matrix.

In this given condition,

order of matrix = m x 1.

where m is any natural number N

So,

Number of rows are m and

Number of columns = 1.

This type of matrix is called Column matrix.

and represents as :

$\bf \: C \: = \begin{pmatrix} x _{1} \\x _{2}\\. \\ . \\ . \\ x _{m} \end{pmatrix}</p><p></p><p>$

This type of matrix is consists of a single column only.

Transpose of a colum matrix is a Row matrix. R.

whose order is 1 x m.

so

$\bf \: C^T \: = \begin{pmatrix} x _{1} \\ x _{2} \\ . \\ . \\ . \\ x _{m} \end{pmatrix}^T = \begin{pmatrix} x _{1} & x _{2} & ... & x _{m} \end{pmatrix} = R$

So, The type of given matrix of order m x 1 is a Column matrix.