Matrices -(MCQ-1) online test

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Types of Matrix

Row Matrix:

A matrix is said to be row matrix if it has only one row. 

Eg  : 

    

Column Matrix:

A matrix is said to be column matrix if it has only one column. 

 Eg:             

   

Square Matrix:

A matrix is said to be Square matrix if number of rows is equal to number of columns.

Thus a matrix of order m x n is said to be square matrix if m= n.

Eg :        



( Number of rows = Numbers of columns )

Diagonal matrix :

A square matrix is said to be a ‘ diagonal matrix’  if its all non-diagonal elements are zero.

Eg:         

        

Scalar matrix :

A diagonal matrix is said to be a ‘scalar matrix’ if its diagonal elements are equal.

Eg:    

Identity matrix:

A square matrix in which elements in the diagonal are all 1 and rest are all Zero is called an ‘Identity matrix’. Identity matrix is denoted by In, where n is the order of the matrix.

 Eg:     

Zero matrix:

A matrix said to be zero matrix or null matrix if all its elements are zero.

Eg:     

EQUALITY OF MATRICES:-

Two matrices A = a_ij  and B = b _ij  are said to be equal, if

(i) Order of A and B are

(ii) Each element of A is equal to corresponding element of B

  that is a _ij = b _ji ∀ i and j.

Eg : If 

  Then  x = 2 ,  y =4 ,  z  =1 ,  a=5.

ADDITION OF TWO MATRICES:

Two matrix can be added or subtracted only if order of both matrix are equal.

·         If A and B are two matrices of order m × n then Addition of A and B is also a matrix of order  m × n whose elements are addition of elements of A with corresponding elements of B.

·         If A = [a_ij]_{m x n} , B = [b_ij ]_{m x n} Then, A + B = [a_ij +b_ij ] _{m x n .}

Subtraction of two matrices:

·         If A and B are two matrices of order m × n then Subtraction  of A and B is also a matrix of order  m × n whose elements are subtraction  of elements of A with corresponding elements of B.

·         If A = [a_ij]_{m x n} , B = [b_ij ]_{m x n} Then, A - B = [a_ij  - b_ij ] _{m x n .}

Properties of matrix addition:

·         Commutative property:  A + B = B+A .

·         Associative property  :  (A + B )+ C = A +(B +C)

·         Additive identity : A + 0 = 0 + A =A

·         Additive inverse : A + ( -A ) = (-A) + A = 0