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TYPES OF MATRICES

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Column Matrix

typesofmatrices1

A matrix is said to be a column matrix if it has only one column.  In general, a = [aij] m x 1 is a column matrix of order m x 1
                      
For example:     typesofmatrices2
                               
Order of A is 3 x 1 and that of B is 4 x 1

Row Matrix

A matrix is said to be a row matrix if it has only one row.  In general,           B = [bij] 1 x n is a row matrix of order 1 x n

For example: A = [2  0  5  -3]        B = [1/2  0   √3     6    7]
Here order of A is 1 x 4 and that of B is 1 x 5

Square Matrix

A matrix whose numbers of columns are equal to number of rows is said to be a square matrix.  Thus an m x n matrix is said to be a square matrix if m = n and is known as a square matrix of order ‘n’.
                                
For example:   typesofmatrices3 
                                                                  
Hence A is of order 3 and B is of order 2.

Diagonal Matrix

A square matrix B = [bij]mxm is said to be a diagonal matrix if all its non diagonal elements are zero.
                                                         
For example: typesofmatrices4
                                     

Hence the orders of A, B and C are 1,2 and 3 respectively

Scalar Matrix

A diagonal matrix is said to be a scalar matrix if its diagonal elements are equal.
That is bij = 0, when i ≠ j
           bij = k, when i = j, for some constant k
                                                                  
For example: typesofmatrices5
Hence the order of A, B and C are 1, 2 and 3 respectively.

Identity Matrix

A square matrix in which elements in the diagonal are all 1 and rest all are zero is called and identity matrix.  In other words, the square matrix A =

typesofmatrices6

Zero Matrix


A matrix is said to be a zero matrix if all its entries are zero.  Another name for zero matrix is null matrix.  It is denoted by 0.
                                       
For example:    typesofmatrices7
The orders of the above matrices are 1 x 1, 2 x 2 and 2 x 3 respectively.

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