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INDEX
Sr.No Topic Name Page number
Introduction to MATLAB 7 1 Starting of MALAB
1.1 MATLAB windows
1.2 Display formats 1.3 Built in functions
1.4 Rules of variables 1.5 Predefined variables
1.6 Managing variables
2 Creating Arrays
2.1 One dimensional (Vector)
2.2 Two dimensional (Matrix) 2.3 Array addressing
2.4 Built in function 2.5 Strings & Strings as variables
2.6 Assignment-I
3 Mathematics operation with array
3.1 Addition & Subtraction 3.4 Multiplication
3.5 Division 3.6 Element by element operation
3.7 Built in functions 3.8 Generation of random numbers
3.9 Assignment- II
4 File
4.1 Script
4.2 Functions 4.3 Assignment-III
5 Plotting
5.1 2D&3D plot
5.2 Assignment-IV
6 MATLAB programming
6.1 Relational operators
6.2 Logical operator 6.3 Built in functions
6.4 Assignment V
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1. Starting with MATLAB
Why MATLAB
Numeric computation software
High level language Basic data type matrix
Dimensioning is not required No compilation or linking
High accuracy guarantee Graphics is incorporated
Varies toolboxes in variety of domain Computations are performed in complex valued double precision
arithmetic
1.1 MATLAB Windows
Table 1.1 MATLAB windows
Sr.No Window Purpose
1 Command
Main window, enters variables, runs
programs.
2 Figure
Contains output from graphic
commands.
3 Editor
Creates and debugs script and function files.
4 Help
Provides help information.
5 Launch Pad Provides access to tools, demos, and
documentation.
6 Command History Loges commands entered in the
Command window.
7 Workspace Provides information about the variables that are used.
8 Current Directory Shows the files in the current directory.
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1.2 Display formats
Table 2.1 Display formats
Sr.No Command Description
1 format short Fixed-point with 4 decimal digits for: 0.001<=number <=1000 Otherwise
display format short e.
2 format long
Fixed-point with 14 decimal digits for:
0.001<=number <=100 Otherwise display format long e.
3 format short e Scientific notation with 4 decimal digits.
4 format long e Scientific notation with 15 decimal digits
5 format short g Best of 5-digit fixed or floating point.
6 format long g Best of 15-digit fixed or floating point.
7 format bank Two decimal digits.
8 format compact Eliminates empty lines to allow more lines with information displayed on the
screen.
9 formats loose Adds empty lines (opposite of compact).
1.3 Elementary functions
Sr.No Function Description Example
1 sqrt(x) Square root >> sqrt(81) ans = 9
2 exp(x) Exponential (ex) >> exp(5) ans = 148.41
3 abs(x) Absolute value >> abs(-24)
ans = 24
4 log(x) Natural logarithm
base e logarithm (ln)
>> log(1000)
ans = 3.00
5 log10(x) base 10 logarithm >> log10(1000) ans = 3.00
6 Factorial(x) The factorial function x! (x must be + ve
integer)
>> factorial(5) ans = 120
Trigonometric
Sr.No Function Description Example
1 sin(x) Sin of angle (x in
radians)
>> sin(pi/6)
ans = 0.5
Note: - Syntax for cosine, tangent, cotangent etc is same.
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Rounding function
Sr.No Function Description Example
1 round(x) Round to nearest
integer
>> round(17/5)
ans = 3
2 fix(x) Round towards zero >> fix(13/5) ans = 2
3 ceil(x) Round towards infinity >> ceil(11/5) ans = 3
4 floor(x) Round towards minus
infinity
>> floor(-9/4)
ans = -3
5 rem(x) Returns remainder after
x is divided by y
>> rem(13,5)
ans = 3
6 sign(x) Signum function.
returns 1 if x>0, -1if
x<0, 0 if x = 0
>> sign(5)
ans = 1
Rules for MATLAB
If a semicolon (;) is typed at end of command output of the
command is not displayed. To write comment % sign at the beginning of line
Using command clc command , it clears command window If command is to long to fit in one line , it can be continued to the
next line by typing three periods … (Called an ellipsis)
1.4 Rules of variables
Variable names can be to 63 (in MATLAB 6.5) characters long (31
characters in MATLAB 6.0 Can contain letters, digits and underscore character
Must begin with letter
MATLAB is case sensitive Avoid using names of built-in functions (sin, cos etc)
Command can be of 4096 characters
1.5 Predefined variables
A number of frequently used variables are already defined when MATLAB
is started.
Ans : If the user does not assign the value of an expression to a variable MATLAB Automatically stores the result in ans.
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Pi : The number Π (22/7 or 3.14)
Eps : The smallest difference between two numbers.
Inf : used for infinity.
i : defined as √-1, which is 0+1.0000i.
NaN : stands for not a number (0/0) (Syntax is CAPITAL -small- CAPITAL)
1.6 Managing variables:
Command outcome
Clear Removes all variables from the memory
Who Displays a list of variables currently in
the memory
Whos Displays a list of variables currently in
the memory
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2. Creating Arrays
2.1One dimensional (Vector) Row vector
A = [ 1 2 3 4 5 6 ]; Or using single space between two numbers
A = [1,2,3,4,5,6]; Or using single comma between two numbers
A = [1:1:6]; Or Syntax: variable_name = [start : step : final]
A = [1:6]; Or Syntax: variable_name = [xi : xf]
A = linspace (1,6,6); Syntax: variable_name = linspace (xi, xf,n)
Column Vector
A = [ 1; 2; 3; 4; 5; 6 ];
2.2 Two dimensional (Matrix) A(i, j) = ith row & jth column
A = [1 2 3; 2 3 4; 5 6 7];
1 2 3
A = 2 3 4
5 6 7
2.3 Array addressing
A = [1 2 3; 2 3 4; 5 6 7];
1 2 3 A = 2 3 4
5 6 7
A (1,2) = 2 A(i, j) = ith row & jth column
A ( : , n ) = Refers to the element in all the rows (:) of column n
A ( n , : ) = Refers to the element in all the columns (:) of row n
A( : , m : n) = Refers to the element in all the rows (:) between columns
m & n
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A( m : n ,:) = Refers to the element in all the columns (:) between rows
m & n
A( m : n , p: q) = Refers to the element in rows m through n & Columns
p through q
2.4 Built in functions for handling arrays
Sr.No Function Description Example
1
length(A) Return no of element in the
vector
>>A = [1 2 3]; >>Length (A)
ans = 3
2
size(A) Returns a row vector [m,n]
>>A= [1 2 ;3 4] >>size(A)
ans = 2 2
3
reshape(A,m,n) Rearrange a matrix
A that has r rows& s columns to have
m rows & n columns. r times s
must be equal to m times n
>>A= [1 2 6 ;3 4 5]
>>B = reshape(A, 3, 2) B =
1 4 3 6
2 5
4
diag (a)
Note small a is
variable other than A
When a is a vector
creates a square matrix with the
elements of A in the diagonal
>>a = [1 2 3 ];
>>A =diag(a) A =
1 0 0 0 2 0
0 0 3
5
diag (A)
When A is a matrix,
creates vector from diagonal elements
of A
>>A= [1 2 3;4 5 6;7 8
9 ]; >>B =diag(A)
B =
1 5
9
Note : For diag direction is always
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2.5 Strings & Strings as variable
A string is an array of characters. It is created by typing the
characters within single quotes.
String can include letters, digits, other symbols, and spaces Examples of strings: „ad ef ‟, „3%fr2‟,‟ {edcba:21!‟, „MATLAB‟.
A string that contains a single quote is created by typing two single quotes within the string.
When a string is being typed in, the color of the text on the screen changes to purple when the first single quote is typed.
When the single quote at the end of the string is typed the color of the string changes to maroon.
Strings have several different uses in MATLAB. They are used in output commands to display text messages, in formatting
commands of plots, and as input argument of some function. When strings are being used in formatting plots, characters
within the string can be formatted to have a specified font, size, position, .color, etc.
Assignment- I
Q.1 Create a row vector that has the elements 32, 4, 81, e2.5, 63, cos
(Π/3) & 14.12
Q.2 Create a column vector that has the elements : 55, 14, ln(51), 987, 0 & 5sin(2.5 Π )
Q.3 Create the following matrix 6 43 2 11 87
A = 2 6 34 0 5 34 18 7 41 9
a) Create a five element row vector named va that contains
the elements of second row of A. b) Create a three element row vector named vb that contains
the elements of fourth column of A. c) Create a ten element row vector named vc that contains
the elements of the first &second rows of A. d) Create a six element row vector named vd that contains
the elements of second & fifth columns of A.
Q.4 Using Zeros and Ones commands create a 3x5 matrix in which
the 1st ,2nd & 5th columns are 0‟s and 3rd ,4th columns are 1‟s.
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3. Mathematics operation with array
3.1 Addition & Subtraction
11 12 13
21 22 23
31 32 33
a a a
A a a a
a a a
&
11 12 13
21 22 23
31 32 33
b b b
B b b b
b b b
Addition
11 11 12 12 13 13
21 21 22 22 23 23
31 31 32 32 33 33
a b a b a b
C A B a b a b a b
a b a b a b
Subtraction
11 11 12 12 13 13
21 21 22 22 23 23
31 31 32 32 33 33
a b a b a b
C A B a b a b a b
a b a b a b
3.2 Multiplication
The product of the multiplication of two square matrices is also square
matrix of the same size. The multiplication of matrices is not
commutative. A*B ≠ B*A
11 12
21 22
a aA
a a
11 12
21 22
b bB
b b
11 11 12 21 11 12 12 22
21 11 22 21 21 12 22 22
*a b a b a b a b
C A Ba b a b a b a b
3.3 Division
Take A & B matrix. Where B is inverse of A (A-1). Then multiply A*B
AI = IA = A & BA = AB =I Two types of division is possible
Left division AX = B;
A-1 AX = A-1B but A-1 AX = IX = X Hence X = A-1B means X = A\B
Right division XA = B;
X A A-1 = B A-1 Hence X = B A-1 means X = B/A
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3.4 Element by element operations All possible operations with matrices can be done or limited by element by
element operations. These operations can be done by putting dot before any multiplication (.*), division (. / or.\), or exponentiation (. ^).
a = [a1 a2 a3 a4] & b = [b1 b2 b3 b4]
Example:
a .*b = [ a1b1 a2b2 a3b3 a4b4]
a ./ b = [a1/b1 a2/b2 a3/b3 a4/b4]
a .^ b = [ (a1)b1 (a2)b2 (a3)b3 (a4)b4]
3.5 Built in function for mathematics
Sr.N
o
Function Description Example
1
mean(A) If A is a vector, returns the
mean value of the elements of the vector.
>> A=[5 9 2 4];
>> mean (A) ans = 5
2
C=max(A)
[d, n] = max(A)
If A is vector, C is the largest element in A. If A is a matrix, C is a row vector containing the
largest element of each column of A.
If A is vector, d is the largest element in A, n is the position of the element (the first if
several have the max value).
>> A=[5 9 2 4 11 6 7 11 0 1]; >>C = max(A)
c=11
>>[d, n] = max(A) d =
11 n =
5
3
Min(A)
[d, n]=min(A)
The same as max (a), but for
the smallest element. The same as [d, n] = max (A), but for the smallest element.
>> A=[5 9 2 4];
>> min(A) ans = 2
4
Sum (A) If A is vector, returns the sum of the elements of the vector.
>> A = [5 9 2 4]; >> sum(A)
ans = 20
5
Sort (A) If A is vector, arranges the elements of the vector in
ascending order.
>> A= [ 5 9 2 4]; >> sort(A)
ans = 2 4 5 9
6 Median (A) If A is vector, returns the
median value of the elements of the vector.
>> A = [ 5 9 2 4]; >> median(A) ans =
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4.5000
7
Std (A) If A is vector, returns the standard deviation of the element of the vector.
>> A = [ 5 9 2 4]; >> std(A) ans=
2.9439
8
det (A) Returns the determination of a
square matrix A.
>> A = [2 4; 3 5];
>> det(A) ans=
-2
9
dot (a, b) Calculates the scalar (dot)
product of two vectors a and b. The vectors can each be row or column vectors.
>> a=[1 2 3];
>>b=[3 4 5]; >> dot (a,b) ans = 26
10
Cross (a, b) Calculates the cross product of
two vectors a and b,(a x b) The vectors must have 3
elements.
>> a=[1 3 2];
>>b=[2 4 1]; >> cross(a,b)
ans = -5 3 -2
11
Inv (A) Returns the inverse of a square
matrix A.
>> A= [2 -2 1;3 2 -1 ;
2 -3 2]; >> inv(A) ans= 0.2 0.2 0
-1.6 0.4 1 -2.6 0.4 2
3.6 Built in function for random number
A set of numbers can be a random number. The rand command generates
uniformly distributed numbers with values between 0 & 1.The command can be used to assign these numbers to a scalar, vector, or a matrix
Sr.No Function Description Example
1
rand Generates a single
random number between 0 and 1.
>> rand
ans = 0.2311
2
rand(1, n) Generates an element n elements row vector of random number
between 0 and 1.
>>a = rand(1,4) a = 0.6068 0.4860 0.8913
0.7621
3
rand (n) Generates an n x n
matrix with random number between 0 and
1.
>> b = rand(3)
b = 0.4565 0.4447 0.9218
0.0185 0.6154 0.7382 0.8214 0.7919 0.1763
4
rand (m, n)
Generates an m x n matrix with random number between 0 and
1.
>> c = rand(3) c =
0.4057 0.9169 0.8936 0.352
0.9355 0.4103 0.057 0.813
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5
randperm (n)
Generates a row vector with n elements that
are random permutation of integers
1 through n.
>> ranperm(8) ans =
8 2 7 4 3 6 5 1
Some time there is need to have random numbers that are distributed in
an interval other than (0, 1) or to have numbers that are only integers. The random numbers that are distributed in a range (a, b) can be
obtained by multiplying rand by (b-a) and adding the product to a (b - a)*rand + a
Example:- A vector of 10 elements with random values between (a = -5) and
(b = 10) can be created as above equation
r = 15*rand (1, 10)-5 r = -1.8 0.6973 6.7499 5.2122 1.9164 3.5174 6.9132 -4.1123
4.0430 -4.2460
Assignment- II
Q.1 The depth of well ,d,in meters can be determined from the time it
takes for a stone that is dropped into well (zero intial velocity) to hit the bottom by d= 0.5 x g x t2, where t is the time in seconds
and g=9.81m/s2. Determine d for t= 1 to 10s.(create a vector t and determine d using element by element calculations.
Q.2 Use the following matrices A, B, C to find
5 2 4
1 7 3
6 10 0
A
11 5 3
0 12 4
2 6 1
B
7 14 1
10 3 2
8 5 9
C
a) Does A*B = B*A ?
b) Does A*(B*C) = (A*B)*C ? c) Does (A*B)t = Bt*At ? (t means transpose)
d) Does (A+B)t = At +Bt ? (t means transpose)
Q.3 Solve the following system of four linear equations
5x+4y-2z+6w = 4 3x+6y+6z+4.5w = 13.5
6x+12y-2z+16w = 20 4x-2y+2z-4w = 6
Q.4 Use matrices from Q.2 for the following hence solve a) Calculate A+B and B+A to show that addition of matrices is
commutative. b) Calculate A+(B+C) and (A+B)+C to show that addition of
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matrices is associative. c) Calculate 5(A+C) and 5A+5C to show that , when matrices
are multiplied scalar , the multiplication is distributive. d) Calculate A*(B+C) and A*B+A*C to show that matrix
multiplication is distributive.
4. File
4.1 Script
A script file is a sequence of MATLAB commands also called
program. When script file runs, MATLAB executes the commands in the order
they are written just as if they were typed in the command window. When a script file has command that generates as output (e.g.
assignment of a value to a variable without semicolon at the end ), the output is displayed in the command window.
Using script file is convenient because it can be edited and executed several times
Script files are also called as M-files .It uses extension .m when they saved.
4.1.1 Creating
% This script file calculates the average points scored in three
games. % The points from each game is assigned to the variable by input
command. % The disp command is used to display the output.
g1=input('Enter the points scored in 1st game '); g2=input('Enter the points scored in 2nd game ');
g3=input('Enter the points scored in 3rd game '); ave=(g1+g2+g3)/3 ;
disp(' ') disp('The average of points scored in a game is :')
disp(' ') disp(ave)
4.1.2 Saving
Save this file with any name (not number) at default folder „work‟ which
located at C:\MATLAB7\work check the same path at MATLAB7 window current directory location.
4.1.3 Running After saving go to debug menu and click on run or save and run (if not
saved earlier).
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4.1.4 Outing Using disp command we are outing result .The command window will look
like as Enter the points scored in 1st game 5
Enter the points scored in 2nd game 4 Enter the points scored in 3rd game 5
The average of points scored in a game is :
4.6667 We can use fprintf('The average of point scored in the three games%f
',ave); in place of disp
4.2 Function
Function files are m-files .That are used to create new MATLAB functions. Variables defined and manipulated inside a function file are
local to function. The general form of function file is
Function variable (s) = function_name(argument)
% help text in the usage of the function %
.
.
end
4.2.1 Creating Ex- Write a function file to solve the equivalent resistance of series
connected resistor R1, R2, R3, R4….Rn R = R1+R2+R3+…..+Rn
Function req =equiv_sr (r) % equiv_sr (r) is a function program for obtaining the equivalent
resistance of series connected resistor % Usage : req = equiv_sr(r)
% r is input vector of length n
% req is an output, the equivalent resistance (scalar) n=length(r); % number of resistance
req = sum(r); % sum of resistor end
4.2.2 Saving Save this file with equiv_sr.m (not number) at default folder „work‟ which
located at C:\MATLAB7\work check the same path at MATLAB7 window current directory location.
4.2.3 Running After saving go to command promt >> use the function as shown
>>a=[1.1 100 2.2 14]; >> series=equiv_sr(a)
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4.4.4 Outing
series = 117.3000
Assignment- III
Q.1 Write a program in a script file that determines the real roots of a quadratic equation ax2+bx+c=0. Name the file quadroots. When
the file runs it asks the user to enter the values of the constants a, b, and c.To calculate the roots of the equation the program
calculates the discrimination D given by: D= b2-4ac
If D >0 the program displays a message “ the equation has two
roots”, and the roots are displayed in the next line. If D = 0 the program displays a message “ the equation has one
root”, and the roots are displayed in the next line. If D<0 the program displays a message “ the equation has no
real roots”, and the roots are displayed in the next line. Run this file in command window to obtain solution for
X2+3x+2=0 15X2+10x+5=0
x2-2x+3=0 Q.2 Write a function file that can be used to calculate the equivalent
resistance of n parallel connected register
1 2 3
1 1 1 1 1........
eq nR R R R R
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5. Plotting
5.1 2D PLOTS
MATLAB has built in functions that allow one to generate bar charts, X-Y polar, contour and 3D.
MATLAB also allows one to give titles to graph, label the X-Y axes and add grid to graphs.
Syntax : Plot (x,y)
: plot(x, y,‟ line specifier‟, „property name‟, property value)
Line specifier It is an optional. It can be used to define the style & color of
line and type of marker
Line style Specifier
Dotted :
Dash-dot -.
Line color Specifier
Red r
Green g
Blue b
Cyan c
Magneta m
Yellow y
Black k
white w
Function Plot
Bar (x,y) Vertical bars
Barh (x,y) Horizontal bars
Stairs(x,y) Stairs case nature
Stem(x,y) Sampled
graph
Pie(x) Pie chart
5.1.1 Multiple plots on one graph 1) „hold all‟ command can be used.
2) Subplot (x, y, position)
Line style Specifier
Solid (default)
-
dashed --
Marker type Specifier
Plus sign +
Circle O
Asterisk *
Point .
Square S
Diamond D
Five pointed P
Six pointed
star
h
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5.2 3D PLOTS
Mesh & surface plot
%This program plots 3D for given function x=-3:0.25:3;
y=-3:0.25:3; [X,Y]=meshgrid(x,y);
Z=1.8.^(-1.5*sqrt(X.^2+Y.^2)).*cos(0.5*Y).*sin(X); mesh(X,Y,Z)
xlabel('x');ylebel('y');zlebel('z')
Some other types
Sr.No Plot type Syntax Example
1 Mesh plot
Mesh(x, y, z) Use above
2 Surface plot
surf(x, y, z) Use above example ;replace mesh(X,Y,Z) by
surf(X,Y,Z)
3
Mesh and
curtain plot
Meshz(X,Y,Z) Draws curtain around the
mesh. Use above example.
4
Mesh and
contour plot
Meshc(X,Y,Z) Draws contour beneath
the mesh. Use above example.
2,2,1 2,2,2
2,2,3 2,2,4
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5
Surface
and contour
plot
Surfc(X,Y,Z) Draws contour beneath
the surface. Use above example.
6
Surface
plot with lighting
Surf1(X,Y,Z) Use above example.
7
Waterfall
plot
Waterfall(X,Y,
Z)
Draws a mesh in one
direction only. Use above example.
8 3D contour Contour3(X,Y,
Z,n) Where n is the number of contour levels. Use above
example
9 2D contour Contour(X,Y,Z
,n) Where n is the number of contour levels. Use above
example
Plot with special graphics
Sr.No Plot type Syntax Example
1
sphere
Sphere(n) Returns the x,
y, z coordinates of a unit sphere
with 20faces
[X,Y,Z]=sphere(20); surf(X,Y,Z)
2
cylinder Cylinder(r) Returns the x,
y, z coordinates of a cylinder
with profile r
t = linspace(0, pi,20); r=1+sin(t);
[X,Y,Z]=cylinder(r); surf(X,Y,Z)
axis square
3
3D bar plot Bar3(Y)
Each element in
Y is one bar. columns are
grouped together
Y = [1 6.5 7;2 6 7; 3
5.5 7; 4 5 7;3 4 7;2 3
7;1 2 7]; Bar3(Y)
4
3D stem Stem3(X,Y,Z) Draws
sequencetial points with
markers and
vertical lines from the X-Y
plane
t =0:0.2:10 x=t;
y=sin(t) z=t .^1.5;
stem(x,y,z,‟fill‟)
grid on
5 3D scatter Scatter3(X,Y,Z)
Removes
t =0:0.2:10
x=t;
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vertical lines
from stem plot.
y=sin(t)
z=t .^1.5; scatter3(x,y,z,‟filled‟)
grid on
6
3D pie Pie3(X,
explode) Plots pie charts
X= [5,9,14,20];
explode =[0 0 1 0]; Pie3(X,explode)
Assignment- IV
Q.1 Plot sin and cos function on same graph. Use linspace command to generate steps?
Q.2 Plot polar graph for r= sin2 (Φ)
Q.3 A message signal m(t) and the carrier signal c(t) of a communication system are respectively
m(t) = 4cos(120Πt)+2cos(240Πt) c(t) = 10cos (10000Πt)
A double sideband suppressed carrier s(t) is given as S(t) = m(t)c(t)
Plot m(t), c(t) and s(t) using the subplot command
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6. MATLAB programming
6.1 Relational & logical operators
A relational operator compares two numbers by determining
whether a comparison statement is true or false.
Sr.No Relational operator Description
1 < Less than
2 > Greater than
3 <= Less than or equal to
4 >= Greater than or equal to
5 = = Equal to
6 ~ = Not equal to
Note: More important in order of precedence type mathematics
numericals. Example:
>> 5>8 ans =
0 (false) Logical operators have numbers as operands. A nonzero number is
true, and a zero number is false.
Sr.No Logical operator Description
1 & ANDing
2 | ORing
3 ~A NOT
Precedence
Precedence operation
1 highest Parentheses
2 Exponentiation
3 Logical not
4 Multiplication/ division
5 Addition/ Subtraction
6 Relational operators
7 Logical AND
8 Logical OR
These are some built in functions
And (A,B), or (A, B), not (A), xor (a, b), all(A), any(A), find (A), find(A>d)
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Assignment- V Q.1 Evaluate the following expressions without using MATLAB. Check
the answer with MATLAB. a) 5< = 8-3
b) y = 7<3-1+6>2
c) y = (7<3) -1+(6>2) d) y = 2x4+5 = = 7 + 20/4
Q.2 Write a user defined the function that sorts the elements of a vector (of nay length) from largest to smallest for the function
name and arguments use Y= downsort(X) .The input to the function is vector X of any length and output Y is vector in which
elements of X are arranged in descending order .Do not use the MATLAB sort function test your function on a vector with 14
numbers (integers) randomly distributed between -30 and 30. Use MATLAB rand function to generate the initial vector.