Matrix is close to singular or badly scaled.
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I'm using MATLAB for some homework problems. One such problem:
consider the vectors:
u1 = [5,8,7,12,11]'
u2 = [2,0,8,8,12]'
u3 = [4,6,10,0,0]'
u4 = [6,8,0,4,0]'
u5 = [18,16,24,32,36]'
If the following vector in the span of the above collection?
b = [23,23,33,29,32]'
So, I make a matrix, and test it, like so:
A = [u1,u2,u3,u4,u5]
A\b
I get the following output:
Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 1.331141e-18
ans =
1.0e+14 *
0
4.0097
0
-2.6731
1.3366
May I basically conclude that it is not in the span of the collection? I tried a similar method with other vectors and got precise answers with no warning.
I'm a little concerned about the warning, and I'm certain my professor doesn't expect answers with 14 decimal places.
Could someone please explain the warning? Also, what does the RCOND mean?
Thanks!
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Risposta accettata
Matt J
il 5 Ott 2012
Modificato: Matt J
il 5 Ott 2012
A hint about your original problem: What can you deduce from the following?
>> rank([A,b])
ans =
5
As for the meaning of RCOND, it is a way of quantifying how invertible a matrix is. Formally, it is the reciprocal of the condition number of A, which you can read about here,
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