## HOW TO FIND SYMMETRIC AND SKEW SYMMETRIC MATRICES

##
**CAN YOU SOLVE THIS PUZZLE ?**

At the end of this post, we shall be able to solve or crack this type of quiz, puzzle, or brain teaser.

Let us discuss the symmetric and skew
symmetric Matrices, How to know whether any given matrix is symmetric or skew symmetric and How to construct 2 × 2 and 3 × 3
Matrix which are Symmetric Matrix
And Skew Symmetric Matrix. Before we proceed we must know what is Transpose Of a Matrix .

###

Symmetric Matrix

Any square matrix is said to Symmetric Matrix if the transpose of that Matrix is equal to the matrix itself. That is if we transform all the Rows of the Matrix into respective column, even then we get same Matrix . Let us discuss this with the help of Some Examples.

**How to Construct 2 × 2 Symmetric Matrix**

1 Complete the 1

^{st}Row of the matrix with the elements of your choice.
2 Copy all Elements which are in 1

^{st}Row to 1^{st}Column.
3 Now place last element in
2

^{nd}Column of 2^{nd}Row with your choice.
The Matrix so obtained is Symmetric Matrix.

As Transpose of these Matrices are equal the Matrices itself, Therefore these Matrices are Symmetric Matrix .

###
**How to Construct 3 × 3 Symmetric Matrix**

1 Complete the 1

^{st}Row of the matrix with the elements of your choice.
2 Copy all
Elements which are in 1

^{st}Row to 1^{st}Column.
3 Complete the 2

^{nd}Row of the matrix with the elements of your choice.
4 Copy all
Elements which are in 2

^{nd}Row to 2^{nd}Column.
5
Put the last element
in the 3rd Column of 3

^{rd}Row of your choice.
The Matrices so obtained are Symmetric
Matrices.

As Transpose of these Matrices are the Matrices itself, Therefore these Matrices are Symmetric Matrices.

## Read Shortcut to find 2×2 and 3×3 Inverse Matrices in a easy way.

##

Skew Symmetric Matrix

Any square matrix is said to Skew Symmetric Matrix if the transpose of that Matrix is equal to the negative of the matrix. That is if we transform all the Rows of the Matrix into respective columns, even then we get same matrix with change in magnitude. Let us discuss this with the help of Some Examples .

**Watch this video to better understand this concept of symmetric and skew symmetric Matrix**

**How to Construct 2 × 2 Skew Symmetric Matrix**

1 Put all the elements equal to Zero in diagonal positions.

2 Complete the 1

^{st}Row of the matrix with the elements of your choice.
3 Copy all Elements which are in 1

^{st}Row to 1^{st}Column with change in magnitude of each element.
The Matrix so obtained is Skew Symmetric Matrix

As Transpose of each of the Matrix written above is negative of the Matrix itself, Therefore these Matrices are Skew Symmetric Matrices.

## How to Construct 3 × 3 Skew Symmetric Matrix

1 Complete all Diagonal elements of the Matrix with Zero.

2 Complete the
remaining elements the 1

^{st}Row with your Choice
3 Copy all Elements which are in 1

^{st}Row to 1^{st}Column.
4 Complete the
remaining elements of the 2

^{nd}Row of the matrix with the elements of your choice.
5 Copy all Elements which
are in 2

^{nd}Row to 2^{nd}Column with change in magnitude of every element.
6 As the elements in the 3

^{rd}column of 3^{rd}Row is already taken as Zero.###

For 3 × 3 Matrix

The Matrices so obtained are Skew Symmetric Matrices, as the
negative of the Transpose of each Matrices are equal to the Matrices Constructed.

## Conclusion

This post is about Symmetric Matrix And Skew Symmetric Matrix . How to Identify and construct 2 × 2 and 3 × 3 Matrices which are Symmetric Matrix And Skew Symmetric Matrix .If you liked the post then share it with your friends and follow me on my blog to boost me to do more and more for you. We shall meet in next post ,till then BYE.....................