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 =
1.
2.
3.
4.
% 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 =
6.
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=
1.
2.
3.
4.
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.
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 =
2.
3.
4.
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;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.
0. 0.
0. 0.
%creating a Matrix consisting of all Ones
B=ones(4,2)
Result:
B =
1. 1.
1. 1.
1. 1.
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:
3.
disp('The number of columns is')
Result:
The number of columns is
disp(p(2))
Result:
3.
%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 =
4.
%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;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 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).
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UpdatedFeb 12, 2020
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Views4,757
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