MatLab: 
The Language of Technical Computing
 
 
 

• Examples:

 

Solving linear equations:
 

3x+5y+21z = 33
7x+9y -11z = 4
8x -2y -    z = 11

Matrix form:

A = 3   5   21                b = 33       X = x
       7   9  -11                        4               y
       8  -2    -1                      11              z
 

A*X = b    =>      X = A^-1 b = A \ b
 

Matlab command:
 

A=[3 5 21; 7 9 -11; 8 -2 -1]
b=[33 4 11]'
X=A\b
 

 
 

Polynomial Roots:
 

x³-2x-5 = 0
 

P(x)  = 1* x³ + 0* x² -2* x -5
For what x, P(x) = 0 ?

Coefficients as elements of a vector:       p = [ 1 0 -2 -5]

Roots:   r = roots(p)
 

Matlab commands:
 

p=[1 0 -2 -5]
r=roots(p)
 
 
 
 
 

 
 Algorithm Development: Calculate the average of  a data set

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

average=(1+2+3+4+5+6+7+8+9+10)/10
 

Matlab operations:
 

x=[1 2 3 4 5 6 7 8 9 10]                        <=  Define a vector

y=sum(x)/length(x)                       <= Calculate average

 
 
 

Self-designed Matlab function:
 

function y = average(x)
% Average mean of vector elements x=[x1 x2 x3 x4 ... xN]
% x must be a vector.
%
% Step I: check whether x is a vector
%
[m,n] = size(x)
if(~((m = = 1) | (n = = 1) | (m = = 1 & n = = 1))
      error('Input must be a vector')
end
%
% Step II: compute the average
%
y = sum(x)/length(x);