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MATLAB RESOURCES |
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A Matlab tutorial from the University of New Hampshire
Quick introduction to MATLAB
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Defining a Vector |
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>> v = [3 1 1] v = 3 1 1 |
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Defining Matrices |
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>> A = [ 1 2 3; 3 4 5; 6 7 0] A = 1 2 3 3 4 5 6 7 0 |
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Matrix time a vector |
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>> A*v'
ans =
8 18 25 |
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Inverse of a Matrix |
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>> inv(A)
ans =
-2.1875 1.3125 -0.1250 1.8750 -1.1250 0.2500 -0.1875 0.3125 -0.1250 |
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Eigenvalues |
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>> eig(A)
ans =
10.4237 -0.2996 -5.1241 |
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Eigenvectors |
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>> [v,e] = eig(A)
v =
-0.3504 -0.7526 -0.3044 -0.6717 0.6497 -0.3788 -0.6527 -0.1071 0.8740
e =
10.4237 0 0 0 -0.2996 0 0 0 -5.1241 |
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Determinant |
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>> det(A)
ans =
16 |
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Echelon Form ( ROWREDUCE) |
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>> R = rref(A)
R =
1 0 0 0 1 0 0 0 1 |
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rrefmovie(A) |
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Characteristic polynomial |
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>> syms lemda >> det( A -
lemda*eye(3) ) ans = 55*lemda+5*lemda^2+16-lemda^3 |
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Matrix Exponential |
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>> exp(A) ans = 1.0e+003 * 0.0027
0.0074 0.0201 0.0201
0.0546 0.1484 0.4034 1.0966 0.0010 |
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Solve a Differential Equation |
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Solve y' - 4 y = 0
>> dsolve('Dy - 4*y = 0')
ans =
C1*exp(4*t)
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System of Differential Equations |
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x' = 2 x + 3 y y'= x - 2y x(0)=1 y(0)=1
>> sol = dsolve( 'Dx=2*x+3*y','Dy=x-2*y','x(0)=1','y(0)=1')
sol =
x: [1x1 sym] y: [1x1 sym]
>> sol.x
ans =
(-1/14*7^(1/2)+1/2)*7^(1/2)*exp(7^(1/2)*t)- ........
>> t=2.3;
>>subs(sol.x)
ans =
634.7773
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