Solving Matrix Equations Using \

Hi, I have a question which involves using the \ on matrix equations where AX=B.

The matrices that I have are:

 A= 0.1750    0.0372    0.0160    0.0200    0.0590
    0.0080    0.0035    0.0200    0.0600    0.0104
    0.1220    0.0623    0.2670    0.8500    0.4721
    0.6950    0.8970    0.6920    0.0670    0.3287

X=[5;2;4;1.5;0.5]

B=[x1;x2;x3;x4]

Here, if I compute AX=B,

B=[1.0729;0.2222;3.3137;8.3019]

However, say I am given only A and B, and want to calculate X. I used X=A\B but X does not equal what I had before. How can I make X=[5;2;4;1.5;0.5] again? What would I have to do?

Thanks

Answer 1

[Walter Roberson]

You have 4 equations in 5 unknowns. There is no solution that can recover the original coefficients. Your equations only define a vector in 5-space, not a point in 5-space.

Answer 2

[Thorsten]

Because A has fewer rows than columns, the equation is underdetermined, that means that there is no unique solution, but multiple valid ones.

Try

X2 = A\B;
A*X2 - A*X
ans =
 1.0e-14 *
 -0.1110
       0
 -0.1332
       0

So the difference between both solutions is very low, in the range of e-14.