Question

Question: Give numerical examples of: a symmetric matrix; a skew-symmetric matrix; a real matrix; a pure imaginary matrix.

Short answer

The Symmetric matrix is$$\begin{gathered} \left(168 \\ 627 \\ 873\right) \end{gathered}$$

The Skew Symmetric matrix is$$\begin{gathered} \left(095 \\ -903 \\ -5-30\right) \end{gathered}$$

The Real matrix is$$\begin{gathered} \left(198 \\ 917 \\ 871\right) \end{gathered}$$

The Pure imaginary matrix is$$\begin{gathered} \left(\mathrm{i}5+\mathrm{i} \\ -5+\mathrm{i}8\mathrm{i}\right) \end{gathered}$$

Step-by-step solution

Description of matrix.

Symmetric matrix:

The elements present on both sides of diagonal elements are same.

Skew symmetric matrix:

The diagonal elements of matrix are zero and rest elements follows like.

${\mathbf{a}}_{\mathbf{32}}\mathbf{=}\mathbf{-}{\mathbf{a}}_{\mathbf{23}}$

Real matrix:

The diagonal elements are unit and rest elements follow symmetry for e.g.

${\mathbf{a}}_{\mathbf{12}}\mathbf{=}{\mathbf{a}}_{\mathbf{21}}$

Pure imaginary matrix:

All elements of a pure imaginary matrix are imaginary numbers.

 Give an example of symmetric, skew symmetric, real and pure imaginary matrices.

The examples of symmetric, skew symmetric, real and pure imaginary matrices are given below:

Symmetric matrix:

The elements present on both sides of diagonal elements are same for e.g.

${\mathrm{a}}_{21}={\mathrm{a}}_{12},{\mathrm{a}}_{32}={\mathrm{a}}_{23}$

Example:

$$\begin{gathered} \left(168 \\ 627 \\ 873\right) \end{gathered}$$

Skew symmetric matrix:

The diagonal elements of matrix are zero and rest elements follows like.

Example:

$$\begin{gathered} \left(095 \\ -903 \\ -5-30\right) \end{gathered}$$

Real matrix:

The diagonal elements are unit and rest elements follow symmetry for e.g.

Example:

$$\begin{gathered} \left(198 \\ 917 \\ 871\right) \end{gathered}$$

Pure imaginary matrix:

All elements of a pure imaginary matrix are imaginary numbers.

Example:

$$\begin{gathered} \left(\mathrm{i}5+\mathrm{i} \\ -5+\mathrm{i}8\mathrm{i}\right) \end{gathered}$$