Basic operations on Matrices

Aim: To generate matrix and perform basic operation on matrices Using MATLAB Software.

EQUIPMENTS:

PC with windows (Windows 7/8/10).
MATLAB Software

Theory:

%Creating a vector from a Known list of numbers:

A=input('enter the Matrix/Vector Elements')

enter the Matrix/Vector Elements 1 2 3 4

Result:

A = 1 2 3 4

%Creating a vector with constant spacing by specifying the first term, spacing and the last term:

m=input('enter the first term')
q=input('enter the spacing')
%Default value of q is 1
n=input('enter the last term')
B=[m:q:n]

Result:

enter the first term m =2

enter the spacing q = 0.1000

enter the last term n =4

B =

column 1 to 12

2. 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3. 3.1

column 13 to 21

3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.

%Creating a vector with constant spacing by specifying the first and the last terms, and the number of terms:

a=input('enter the first element')
b=input('enter the last element')
c=input('enter the number of elements')
C=linspace (a,b,c)

Result:

enter the first element a =3.

enter the last element b =6.

enter the number of elements c =5.

C = 3. 3.75 4.5 5.25 6

% Creating an All Zero Vector

m=input('enter the number of terms in the vector')
D=zeros(1,m)

Result:

enter the number of terms in the vector m =5.

D =0 0 0 0 0

% Creating a Vector consisting of all Ones

n=input('enter the number of terms in the vector')
E=ones(1,n)

Result:

enter the number of terms in the vector n =6.

E =1 1 1 1 1 1

% Measuring the size(number of elements) of the vector

A=[1 2 3 4]
l=length(A)

Result:

A =1 2 3 4

l = 4.

% Measuring the order of the vector

D= [1 1 1 1 1]
p=size (D)

Result:

D =1 1 1 1 1

p =1 5

disp('The number of rows is')
The number of rows is
disp(p(1))

Result: 1.

disp('The number of columns is')
The number of columns is
disp(p(2))

Result: 5.

% Transpose of a Matrix

A=[1 2 3 4]
A1=A'

Result:

A = 1. 2. 3. 4.

A1 =

% Multiplying each element of the vector/Matrix with a constant

k=input('enter the value of the Multiplying Constant')
B=[3 4 5 6]
B1=k*B

Result:

k =3.

B =3. 4. 5. 6.

B1 =9. 12. 15. 18.

%The above Multiplication operation can be done also as follows:

B11=k.*B

% Finding the sum of elements of a Matrix

A=[1  2.1 3.3  4]
S=sum(A)

Result:

A =1. 2.1 3.3 4.

S =10.4

B =
   1.    2.    3.  
   4.    5.    6.  
   7.    8.    9.  
S1=sum(B)

Result:

S1 = 45.

%Finding the sum of each row and displaying in a column

S2=sum(B, 'c')

Result:

S2 =

15.

24.

% Finding the sum of each column and displaying in a row

S3=sum(B, 'r')

Result:

S3 =

12. 15. 18.

% Finding the average of the elements of Matrix

B=[2  3  4  5]
Ave=mean(B)

Result:

B =2. 3. 4. 5.

Ave =3.5

%Finding the maximum and minimum values of a vector

A=[1  2 3 10.1 -1]
A1=max(A)
A2=min(A)

Result:

A =1. 2. 3. 10.1 - 1.

A1 =10.1

A2= -1

%Finding the product of the elements of a Matrix

A=[1  2  3  4]
P=prod(A)

Result:

A =1. 2. 3. 4.

P =24.

% Checking the sign of the elements of a Matrix

B=[-1 -2 3 4 -5 0]
S=sign(B)

% sign(B) returns 1 if the element of B is +ve, -1 if the element is –ve and zero if the element is zero

Result:

B =

- 1. - 2. 3. 4. - 5. 0.

S =

- 1. - 1. 1. 1. - 1. 0.

% Finding the non zero elements of the Matrix

A=[-1  2  0  0  2  3]
S=find(A)

% find(A) returns the indices of the non- zero elements of A

Result:

A = -1. 2. 0. 0. 2. 3.

S =1. 2. 5. 6.

% Arranging the elements of a Matrix in ascending/descending order

A=[1  23  45  6  73]
A1=sort(A,’ascend’)

Result:

A =1. 23. 45. 6. 73.

A1 =1. 6. 23. 45. 73.

% mtlb_sort(A) also will do the same

A2=sort(A, ’descend’)

Result:

A2= 73. 45. 23. 6. 1.

%Reshaping the Matrix

A=[1 2 3 4]
A1=matrix(A,4,1)
A2=A(:)
A3=matrix(A,2,2)

Result:

A =1. 2. 3. 4.

A1 =A2=

A3 =

1. 3.

2. 4.

% Extending the Dimension of the Matrix

A=[1 2 3]
%Appending a Row
A(2,:)=[4 5 6]

Result:

A =1. 2. 3.

4. 5. 6.

%%Appending a Column

A=[1 2 3]
A(:,4)= 10

Result:

A = 1. 2. 3. 10.

%Deleting the elements of a Matrix

A=[1 2 3 4]
A =1.     2.   3.     4.
% Deleting the 4th column element
A(4)=[ ]

Result:

A =1. 2. 3.

%Arithmetic operations

%Addition of Two row matrices

A=[1 2 3]
B=[5 6 7]
S=A+B
D=A-B

Result:

A =1. 2. 3.

B =5. 6. 7.

S =6. 8. 10.

D = -4. -4. -4.

%Multiplication of Two Matrices

A=[1 2 3]
B=[2;3;4]
C=A*B

Result:

A =1. 2. 3.

B =

C =20

% Element wise Multiplication

A=[1 2 3]
B=[3 4 5]
C=A.*B

Result:

A =1. 2. 3.

B =3. 4. 5.

C =3. 8. 15.

%Element wise Division

A=[1 2 3]
B=[3 4 5]
C=A./B

Result:

A =1. 2. 3.

B =4. 4. 6.

C =0.25 0.4 0.5

C1=A.\B

Result:

C1=3. 2. 1.6666667

%Raising each element of the matrix to 3rd power

A=[2 5 8]

B=A.^3

Result:

A =2. 5. 8.

B =8. 125. 512.

%Relational Operators

A=[1 2 3]
B=[5 3 1]
K=A>B
K1=A<B

Result:

A =1. 2. 3.

B =5. 3. 1.

K = F F T

K1=T T F

A=[1 2 3]
B=[1 3 3]
K=A<=B
K1=A>=B
K2=A==B

Result:

A =1. 2. 3.

B =1. 3. 3.

K = T T T

K1=T F T

K2=T F T

A=[1 2 3]
B=[1 3 3]
K=A~=B( not equal to)

Result:

A = 1. 2. 3.

B = 1. 3. 3.

K = F T F

%Logical Operators

A=[1 2 3]
B=[2 0 4]
K=A|B
K1=A&amp;amp;amp;B

Result:

A =1. 2. 3.

B =2. 0. 4.

x =T T T

y =T F T

A=[1 0 3]
K=~A

Result:

A=1. 0. 3.

K =F T F

%These Programs explain various (MxN) Matrix Operations:

%Creating a One-Dimensional Array/Vector:

A=input('enter the Matrix Elements')

Result:

enter the Matrix Elements[1 2 3;4 5 6;7 8 9]

A =

1. 2. 3.

4. 5. 6.

7. 8. 9.

%creating a Matrix consisting of all zeros

A=zeros(3,2)

A =

0. 0.

%creating a Matrix consisting of all Ones

B=ones(4,2)

Result:

B =

1. 1.

%Creating an Identity Matrix

A=eye(3,3)

Result:

A =

1. 0. 0.

0. 1. 0.

0. 0. 1.

%Measuring the order of the vector

A=[1 2 3;4 5 6;2 3 -1]
p=size(A)

Result:

A =

1. 2. 3.

    4.     5.     6.

2. 3. -1.

p= 3. 3.

disp('The number of rows is')

Result:

The number of rows is

disp(p(1))

Result:

disp('The number of columns is')

Result:

The number of columns is

disp(p(2))

Result:

%Transpose of a Matrix

A=[1 2 3 ;10 11 12; 34 45 89]
A1=A'

Result:

A =

1. 2. 3.

10. 11. 12.

34. 45. 89.

A1 =

1. 10. 34.

2. 11. 45.

3. 12. 89.

%Multiplying each element of the Matrix with a constant

k=input('enter the value of the Multiplying Constant')
B=[3 4 5 6;2 4 6 8]
B1=k*B

Result:

enter the value of the Multiplying Constant

k =4

B =

3. 4. 5. 6.

2. 4. 6. 8.

B1 =

12. 16. 20. 24.

8. 16. 24. 32.

%The above Multiplication operation can be done also as follows:

B11=k.*B

%Finding the sum of element of a Matrix

A=[1  2 ;3 4;5 6]
S=sum(A)

Result:

A =

1. 2.

3. 4.

5. 6.

S =21.

%Finding the average of the elements of Matrix

B=[2 3 4;4 5 6]
Ave=mean(B)

Result:

B =

2. 3. 4.

4. 5. 6.

Ave =

%Finding the maximum and minimum values of a vector

A=[1 2 3; 10  2  -1]
A1=max(A)
A2=min(A)  
P=prod(A)

Result:

A =

1. 2. 3.

10. 2. -1.

A1 =10.

A2 = -1.

P = -120.

%Checking the sign of the elements of a Matrix

B=[-1 -2 3;4 -5 0]
S=sign(B)
%sign(B) returns 1 if the element of B is +ve, -1 if the element  is –ve and zero if the element is zero

Result:

B =

-1. -2. 3.

4. -5. 0.

S =

-1. -1. 1.

1. -1. 0.

%Finding the non zero elements of the Matrix

A=[-1 2 0; 0 2 3]
S=find(A)
%find(A) returns the indices of the non- zero elements of A

Result:

A =

-1. 2. 0.

0. 2. 3.

S = 1. 3. 4. 6.

% checking a matrix whether is empty or not

A=[1 2 3 0]
K= isempty(A)
%isempty() returns a true value for an empty matrix

Result:

A =

1. 2. 3. 0.

K = F

%Arranging the elements of a Matrix in ascending/descending order

A=[1 23 45; 6 7 3]
A1=sort(A,’descend’)
%each column of A is sorted

Result:

A =

1. 23. 45.

6. 7. 3.

A1 =

6. 23. 45.

1. 7. 3.

A1=sort(A, ‘ascend’)
%each row of A is sorted

Result:

A1=

45. 23. 1.

7. 6. 3.

%all the elements of A are sorted in increasing order

A1 =

1. 6. 23.

3. 7. 45.

% all the elements of A are sorted in decreasing order

A1=sort(A, ‘desccend’)

A1 =

45. 7. 3.

23. 6. 1.

%Reshaping the Matrix

A=[1 2 3 4;3 5 6 7]
A1=matrix(A,4,2)
A2=matrix(A,1,8)

Result:

A =

1. 2. 3. 4.

3. 5. 6. 7.

A1 =

1. 3.

3. 6.

2. 4.

5. 7.

A2 =

1. 3. 2. 5. 3. 6. 4. 7.

%Extending the Dimension of the Matrix

A=[1 2 3;4 5 6]

%Appending a Row

A(3,:)=[10 15 26]

Result:

A= 1. 2. 3.

4. 5. 6.

A =

1. 2. 3.

4. 5. 6.

10. 15. 26.

%Appending a Column

A(:,4)=[10;20;87]

A= 1. 2. 3. 10.

4. 5. 6. 20.

10. 15. 26. 87.

%Appending an Intermediate row

A=[1 2 3;4 5 6;7 8 9]

A =

1. 2. 3.

4. 5. 6.

7. 8. 9.

%Appending a row between 1st and 2nd rows

A=[A(1,:); 10 11 12;A(2,:);A(3,:)]

Result:

A =

1. 2. 3.

10. 11. 12.

4. 5. 6.

7. 8. 9.

%Appending a column between 2nd and 3rd column

A=[1 2 3;4 5 6;7 8 9]
A=[A(:,1) A(:,2) [10;12;15;16] A(:,3)]

Result:

A =

1. 2. 10. 3.

10. 11. 12. 12.

4. 5. 15. 6.

7. 8. 16. 9.

%Deleting the row/column of a Matrix

A=[1 2 3; 4 5 6]
%Deleting the 2nd  row  
A(2,:)=[ ]

Result:

A =

1. 2. 3.

4. 5. 6.

A =

1. 2. 3.

%Deleting the 2nd column

A=[1 2 3; 4 5 6]
A(:,2)=[ ]

Result:

A =

1. 2. 3.

4. 5. 6.

A =

. 3.

4. 6.

%Arithmetic operations

%Addition of Two row matrices

A=[1 2 3;4 5 6]
B=[5 6 7;10 11 12]
S=A+B
D=A-B

Result:

A =

1. 2. 3.

4. 5. 6.

B =

5. 6. 7.

10. 11. 12.

S =

6. 8. 10.

14. 16. 18.

D =

-4. -4. -4.

-6. -6. -6.

%Multiplication of Two Matrices

A=[1 2 3;4 5 6]
B=[5 6 3;10 11 12;3 4 6]
C=A*B

Result:

A =

1. 2. 3.

4. 5. 6.

B =

5. 6. 3.

10. 11. 12.

3. 4. 6.

C =

34. 40. 45.

88. 103. 108.

%Element wise Multiplication

A=[1 2 3;4 5 6]
B=[3 4 5;3 2 1]
C=A.*B

Result:

A =

1. 2. 3.

4. 5. 6.

B =

3. 4. 5.

3. 2. 1.

C =

3. 8. 15.

12. 10. 6.

%Element wise Division
C=A./B

Result:

C =

0.3333 0.5000 0.6000

1.3333 2.5000 6.0000

%Raising each element of the matrix to 4th power

A=[2 5 8;4 5 6]
B=A.^4

Result:

A =

2. 5. 8.

4. 5. 6.

B =

16. 625. 4096.

256. 625. 1296.

%Relational Operators

A=[1 2 3;10 3 5]
B=[5 3 1;0 3 6]
K=A>B
x=A<B
y=A<=B
K1=A>=B
K2=A==B
K3=A~=B

Result:

A =

1. 2. 3.

10. 3. 5.

B =

5. 3. 1.

0. 3. 6.

K =

F F T

T F F

x =

T T F

F F T

y =

T T F

F T T

K1 =

F F T

T T F

K2 =

F F F

F T F

K3 =

T T T

T F T

%Logical Operators

A=[1 2 3;0 0 1;1 -1 0]
B=[2 0 4;-1 2 -3;9 8 0]
K=A|B
K1=A&amp;amp;B

Result:

A =

1. 2. 3.

0. 0. 1.

1. -1. 0.

B =

2. 0. 4.

-1. 2. -3.

9. 8. 0.

K =

T T T

T T F

K1 =

T F T

F F T

T T F

A=[1 0 3;2 -1 0;3 2 -1]
K=~A/k=not(A)

Result:

A =

1 0 3

2 -1 0

3 2 -1

K =

F T F

F F T

Viva Questions:

1. What is the command to generate row matrix?

R=[a,b,c]

2. What is the command to generate column matrix?

colvec = [a ; b ; c]

3. What is the command to generate matrix?

matrix=[1,2,3;4,5,6;7,8,9]

4. What is the command to find Inverse matrix?

Inverse_matrix= Inv(m).

Updated
Feb 12, 2020
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