Matrix & ITS Types

MATRIX :

"Matrix is nothing but the rectangular representation of data in the form of rows and columns inside square brackets "

• A row matrix is a matrix that has only one row.
• A column matrix is a matrix that has only one column.

Example :


To convert linear equations into matrix :

Each equation in the system becomes a row. Each variable in the system becomes a column. The variables are dropped and the coefficients are placed into a matrix. If the right hand side is included, it's called an augmented matrix. If the right hand side isn't included, it's called a coefficient matrix.

The system of linear equations ...

 x +  y -  z = 1

3x - 2y +  z = 3

4x +  y - 2z = 9

becomes the augmented matrix ...

	x	y	z	rhs
	1	1	-1	1
	3	-2	1	3
	4	1	-2	9

Type of Matrix :

1. ZERO/NULL Matrix :

2. UPPER  & LOWER TRIANGULAR MATRIX :

3. Diagonal Matrix  :

4. IDENTITY MATRIX:

5. SYMMETRIC MATRIX : 

* If a matrix is equal to its transpose matrix then it is called symmetric matrix.

                                                                  A = A^T

6. SKEW SYMMETRIC 

* If a matrix is equal to the negative of its transpose then it is called SKEW SYMMETRIC 

 A = -A^T

Example of skew symmetric :

7. Idempotent Matrix :

* A square matrix A is called idempotent matrix if   

A² = A

8. Involutory Matrix 

 A² = I