How to find symmetric and skew symmetric matrices

How to find symmetric and skew symmetric matrices  

CAN YOU SOLVE THIS  PUZZLE ?

 If you want to know the answer of this problem , just click here

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   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.

For 2 × 2 Matrix ,

If

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.

For 3 × 3 Matrix ,If

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

For 2 × 2 Matrix,If 

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

If

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.....................

Let us learn Multiplication , division , Arithmetic and simplification short cut ,tips and  tricks after buying this Book of Magical Mathematics .