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

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????

[per isakson]

See mldivide, \, Solve systems of linear equations Ax = B for x

Answer 1

[Roger Stafford]

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.

Answer 2

[MOHIT]

follow this link

http://in.mathworks.com/help/matlab/ref/mrdivide.html