Matrix

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satis · Answer

Q1.
  
For  each matrix below, determine the order and state whether it is a square matrix.
  
Order of a matrix is  (columns  x rows)
  
When  columns = rows  in a matrix,  is called a square matrix.
  
 
  
                        Matrix                                    Order             whether a square matrix 
  
                 2 x 4                           No
                               3 x 3                           A square matrix
                                      1 x 4                           No
                                        2 x 2                          A square matrix
  [3]                                                       1 x 1                           A square matrix
  
 
  
 
  
 
  
 
  
 
  
 
  
Q2.  Given matrices:
  
A =             B =             C =              
  
D =              E = [3],         F = ,    G = 
  
What is the dimension of each matrix ?
  Which matrices are square?
  Which matrices are symmetric ?
  Which matrix has the entry at row 3 and column 2 equal to -11 ?
  Which matrix has the entry at row 1 and column 3 equal to 10 ?
  Which are column matrices ?
  Which are row matrices?
  Find AT, CT, ET, GT
  
Dimension of a matrix is the order of the matrix: row x column
  
A : 2 x 4,        B : 4 x 3,        C: 1 x 3,         D : 2 x 2,        E : 1 x 1,                    F : 1 x 4,         G : 3 x 2
  
 
  
When  columns = rows  in a matrix,  is called a square matrix.
  
The square matrices are :  D and  E 
  
 
  
If the transpose of a matrix is equal to the matrix itself, the matrix is said to be symmetric. 
  
Transpose of a matrix is a matrix obtain by using the rows of the matrix as  column in the transpose matrix.
  
                        Only  matrix  E = [3] is symmetric
  
 
  
Matrix  B
  
 
  
Matrix B
  
 
  
A column matrix  is a matrix consists of a single column.  The dimension of a column matrix  is  rows x 1
  
            Column matrices are :        E  and  F 
  
 
  
A row matrix  is a matrix consists of a single row.  The dimension of a row matrix  is  1 x columns
  
Row matrices are :   C and E
  
Transpose of a matrix is a matrix obtain by using the rows of the matrix as  column in the transpose matrix.
  
 
  
AT  =    ,                                  CT  =  ,    
  
ET  =        [ 3 ],                                               GT =           
  
 
  
 
  
Q3.       Given the matrices :
  
            A =     , B =            ,  C =   ,  
  
D =      ,                     E =               
  
Which of the above matrices are diagonal ?
  Which of the above matrices are lower triangular ?
  Which of the above matrices are upper triangular ?
  
A square matrix in which every element except the principle diagonal elements is zero, it is called a diagonal matrix.
  
            The diagonal matrices are:  matrices C and  E   
 
  
A lower triangular matrix is one which contains all its non-zero elements in and below its main diagonal.
  
            The lower triangular matrix is :  Only matrix B
  
 
  
A upper triangular matrix is one which contains all its non-zero elements in and above its main diagonal.
  
            The lower triangular matrices are : matrices A and D

omsinghpatel · Answer

Solution is detail and define every term which ask in question and all is correct

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