Notes

Type the following in a script file and write down the results.
1.
a=[4 -2 -4 7;1 5 -3 2;6 -8 -5 -6;-7 3 0 1]
size(a)
a(2,3) %returns the element of the matrix in row 2 andcolumn 3.
a(15) %returns 15th position element when the matrix iswritten out as a single column.
inv(a)
a(2,1:3) %lists all values in row 2 which are betweencolumns 1 and 3 inclusive
a(2:4,3) %lists all the values in column 3 which arebetween rows 2 to 4 inclusive.
a(2:3,3:4) %lists all the values which lie between rows 2to 3 and columns 3 to 4.
a(3,:) %lists all the elements along row 3
a(:,2) %lists all the elements along column 2
a(:) %lists all the matrix elements as a single column
b=[2 4 -7 -4;5 6 3 -2;1 -8 -5 -3;0 -6 7 -1];
2*a-3*b %add, subtract and multiply matrices
a^3+b^4 %take matrix powers
c = [3 4 5 6; 6 7 8 9]
d = [8 10 44 999; 0 1 34 55]
c.*d %element to element multiplication
c.^2
d.*d
det(a)
adjoint(a)
inv(a) %inversion is performed using the inv function
a' %transpose is obtained by using the apostrophe
flipud(a) %flip a matrix up/down
fliplr(a) %flip a matrix left/right
2. Realize one dimensional array of real and complex
numbers
a = [1 2 42 50] %row vector
size(a)
c = [1:5:50]
b = [1 2 4 50]' %column vector
size(b)
% Realize one dimensional array of complex numbers
d = [3+5i 7+10i 2-50i]
size(d)
e = [3+5i 7+10i 2-50i].' %compute its nonconjugate transpose
size(e)
f = conj(e)
3. stem and continous plots of real arrays
a = [ 9 8 7 6 5]; % row vector
t = [1 2 3 4 5];
plot(t,a); %continous plot
figure
plot(t,a,'ro')
figure
stem(t,a) %discrete plot
figure
stem(t,a,'b*')
b = [ 5 8 7 6 5]'; % column vector
t = [1 2 3 4 5];
figure
plot(t,b);
figure
plot(t,b,'r+')
figure
stem(t,b)
figure
stem(t,b,'b*')
4. Realization of two dimensional arrays and matrices and
their visualizations
a = rand(100);
imshow(a)
imwrite(a,'myimage1.jpg')
imfinfo('myimage1.jpg')
r = randi([0 50],1000,1000)
imshow(r)
imwrite(r,'myimage2.jpg')
imfinfo('myimage2.jpg')
5. Inverse of a square matrix and the solution of the
matrix equation
a = [1 2 3;4 5 6;7 8 9];
disp('determinant of matrix is');
disp(det(a))
disp('inverse of matrix is');
disp(inv(a))
b = [1 2;1 2]
disp('inverse of matrix is');
inv(b)
a = [1 3 -4; 2 -5 0; -2 -6 8];
b = [0 0 0]'
[x r] = linsolve(a,b)
a = [1 3 -4; 2 -5 8; -3 -6 7];
b = [0 0 0]'
[x r] = linsolve(a,b)
a = [1 2 3; 1 3 4; 2 2 3];
b = [6 8 12]'
[x r] = linsolve(a,b)
a = [1 2 3; 1 3 4; 2 6 8];
b = [6 8 12]'


[x r] = linsolve(a,b)
a = [1 2 3; 1 3 4];
b = [6 8 ]'
[x r] = linsolve(a,b)
6. Computation of the rank ,eigen values of matrix and its
singular value decomposition
a = [2 1 1;1 3 2;3 1 4]
rank(a)
[V D] = eig(a)
[U S V ] = svd(a)
a = [2 -1;-3 2;5 4]
[U S V ] = svd(a)