Matrix is close to singular or badly scaled.

Question

Clark 2012-10-5

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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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Answer 1

Matt J 2012-10-5

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编辑：Matt J 2012-10-5

在 MATLAB Online 中打开

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,

http://en.wikipedia.org/wiki/Condition_number