what does matlab do in A/b if both matrices are 1x4 matrices in order to come up with a number ???

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Manny Ram
Manny Ram 2016-6-18
编辑： Roger Stafford 2016-6-18
Hi There,
I hope any of your answer my question. I am a sophomore at SFSU and I am learning matlab on my own. my question is very simple I have 2 matrix of 1X4. A=[1 2 3 4] and b=[5 6 7 8]. I know if I type A*inv(b) will be an error because the matrix b is not invertible as I learned in linear algebra. But what does matlab exactly do when I type A/b in order to get me 0.4023?? I cant not figure it out. please, I would appreciate your help. How would I get to that number if I am trying to solve it manually????

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回答（2 个）

Roger Stafford
Roger Stafford 2016-6-18
编辑：Roger Stafford 2016-6-18
When you write x = A/b, it is like writing x*b = A, and for this to make sense in your situation as far as size is concerned x must be of 1 x 1 size. Therefore this would a a set of four equations and only one unknown, an overdetermined system. The solution that matlab comes up with is a least squares approximation, since in general you cannot satisfy four equations exactly with only one unknown.
In your particular case with A = [1 2 3 4] and b = 5 6 7 8], the equations would be:
5*x = 1
6*x = 2
7*x = 3
8*x = 4
These obviously have no exact solution, so it finds the x for which
(5*x-1)^2 + (6*x-2)^2 + (7*x-3)^2 + (8*x-4)^2 =
174*x^2 - 140*x + 130
is a minimum. From calculus we know that the minimum occurs at the point where the derivative is zero:
x = 140/(2*174) = 0.402298851
though matlab uses a different method from this.
MOHIT
MOHIT 2016-6-18

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