INVERSE AND ADJOINT OF A MATRIX USING MATLAB

INVERSE OF MATRIX:

matrix inverse can be found out by using the formula

                                               inverse of A = adj(A)/det(A)

adj(A) - adjoint matrix of A

But there is a direct code to find out the Inverse of the matrix

command:
             
               A = [1 4 5; 6 6 8 ; 1 3 7 ]
               B = inv(A)

 the output is

This is how inverse of a matrix can be found.

ADJOINT MATRIX CAN BE FOUND OUT BY

command:  

adj(A) = det(A)*inv(A)

the output is

This is how adjoint matrix can be found 

ROUND,FLOOR,FIX,CEIL COMMANDS

Round:
 Rounds towards nearest integer
COMMANDS:

round(2.3) 

round(2.6)

the output is
 

the output of round(2.3) is 2 because the nearest integer for 2.3 is 2
 the output of round(2.6) is 3 because the nearest integer for 2.6 is 3
 Floor:
 it rounds towards negitive infinity code:

floor(2.7)
the output is

 

output is 2 because nearest integer in the direction of negitive infinity is 2

 ceil:
        it round towards positive infinity code:

ceil(2.3)

output is

  output is 3 because nearest integer in the direction of positive infinity is 3

 fix:
          rounds the number towards zero code:

fix(-1.3) 

fix(1.3)

the output is fix(-1.3) gives output -1 because nearest integer in  the direction of zero is -1
 fix(1.3) give s output 1 because nearest integer in the direction of zero is 1
 These are 4 commands to round numbers

DETERMINANT OF A MATRIX USING MATLAB

determinant of a matrix is used to check the singularity
 singular  if det value is 0
non singular if det value is not zero
it is also used to say about invertibility of a matrix

code for determinant:

a = [ 1 5 7 ; 2 3 4 ; 5 7 3] 

det(a)

The output is

 

by this we can find the determinant of matrix

TRANSPOSE OF MATRIX USING MATLAB

TRANSPOSE OF MATRIX: ( DONE USING 3 X 3 MATRIX)  

Matrix transpose means Interchanging Rows and columns

 code:

a = [1 2 3 ;4  5  6 ; 7 8 9] 

b = a'                                             ("  '  "  is used for transposing)

output is
 

This is how matrix transposing is done

OPERATIONS ON MATRICES USING MATLAB

code for adding two matrices:  ( '+' operator is used for summing two matrices)

a = [ 1 2 3 ; 4 5 6 ; 7 8 9] 

b= [ 1 0 0 ; 0 1 0; 0 0 1] 

c = a+b

code for matrix subtraction: ('-' operator is used for subtraction. It is done using 2x2 matrices)

a = [ 2  2 ; 4  4] 

b = [1   0 ; 0  0] 

c = a-b

multiplying matrices: (' * 'operator is used for multiplication)

a = [ 1  2  ; 3  4 ] 

b = [ 1 0 ; 0  1] 

c = a*b

INTRODUCTION TO MATRICES IN MATLAB

Basics of Matrices Row Matrix  :

row matrix:

a matrix which has only one row.
 example:  [1  2  3]

 column Matrix :

 a matrix which has only one column
 example    [ 1
                      2
                      3 ]

 square matrix:

has equal number of rows and columns

 ex: a=[  2      2
               4     4   ]

 this a 2 x 2 matrix rectangular matrix: matrix which has unequal columns and rows

 ex: a = [2  2  2
              4  4  4 ]

 coding for initializing the each of the above matrices: 

row matrix initializing

a = [1  2  3]                                 (this initilizes a row matrix)

column matrix initializing:

b = [1 ; 2 ; 3]                          (';' is used to end a particular row)

square matrix initializing:

c = [2   2   ;  4   4]

rectangular matrix initializing:

d = [2   2   2 ; 4   4   4]

the output is

OPERATION ON VARIABLES IN MATLAB

code for summing of 2 Variables: (write in m- file or commmand window)

a = 10                             (initilizing "a ") 

b =20                               (initilizing "b")

          c = a+b                             ('+' operator is used for summing two  variables')                                        
this is the code used for summing of 2 variables and storing result in variable c the output  is

 

Subtraction code:

a=10 

b=5 

c=a-b

the output is

 

 multiplying and dividing:

a=10 

b=5  

c=a*b                    ( '*' operator is used for subtraction) 

d=a/b                     (' / ' operator is used for division)

The output is
 

the arthematic operation are performed as shown in above examples