Resolução do problema em MATLAB
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>>
A=[7 8 1;6 4 3;5 5 7]
A
=
7 8
1
6 4
3
5 5
7
>>
b=[25;30;40]
b
=
25
30
40
>>
x=A\b
x
=
3.5217
-0.3913
3.4783
>>
A*x
ans =
25
30
40
>> L=[0 0 0;-6 0 0;-5 -5 0]
L =
0 0
0
-6 0
0
-5 -5
0
>>
U=[0 -8 -1;0 0 -3;0 0 0]
U
=
0
-8 -1
0 0
-3
0 0
0
>>
D=[7 0 0;0 4 0;0 0 7]
D
=
7 0
0
0 4
0
0 0
7
>>
C=inv(D)*(L+U)
C =
0 -1.1429 -0.1429
-1.5000 0 -0.7500
-0.7143 -0.7143 0
>> help norm
NORM Matrix or vector norm.
For matrices...
NORM(X) is the largest singular value of X, max(svd(X)).
NORM(X,2) is the same as NORM(X).
NORM(X,1) is the 1-norm of X, the largest column sum,
=
max(sum(abs((X)))).
NORM(X,inf) is the infinity norm of X, the largest row sum,
= max(sum(abs((X')))).
NORM(X,'fro') is the Frobenius norm, sqrt(sum(diag(X'*X))).
NORM(X,P) is available for matrix X only if P is 1, 2, inf or 'fro'.
For vectors...
NORM(V,P) = sum(abs(V).^P)^(1/P).
NORM(V) = norm(V,2).
NORM(V,inf) = max(abs(V)).
NORM(V,-inf) = min(abs(V)).
See also COND, RCOND, CONDEST, NORMEST.
>> norm (C)
ans =
1.8480
>> help norm
NORM Matrix or vector norm.
For matrices...
NORM(X) is the largest singular value of X, max(svd(X)).
NORM(X,2) is the same as NORM(X).
NORM(X,1) is the 1-norm of X, the largest column sum,
= max(sum(abs((X)))).
NORM(X,inf) is the infinity norm of X, the largest row sum,
= max(sum(abs((X')))).
NORM(X,'fro') is the Frobenius norm, sqrt(sum(diag(X'*X))).
NORM(X,P) is available for matrix X only if P is 1, 2, inf or 'fro'.
For vectors...
NORM(V,P) = sum(abs(V).^P)^(1/P).
NORM(V) = norm(V,2).
NORM(V,inf) = max(abs(V)).
NORM(V,-inf) = min(abs(V)).
See also COND, RCOND, CONDEST, NORMEST.
>> norm(C,1)
ans =
2.2143
>> norm(C,inf)
ans =
2.2500
>> help eing
eing.m not found.
>> eig(C)
ans =
-1.6759
1.3335
0.3425
>> [v,d]=eig(C)
v =
0.5132 0.6457 -0.4514
0.6886 -0.7611 0.0238
0.5122 0.0618 0.8920
d =
-1.6759 0 0
0 1.3335 0
0 0 0.3425