## Return if No Solution

### Allison Bushman (view profile)

on 13 Sep 2019 at 20:37
Latest activity Commented on by Walter Roberson

### Walter Roberson (view profile)

on 13 Sep 2019 at 21:24

### Walter Roberson (view profile)

I am asked to solve the equation: Ax = B for two randomly generated matrices. Furthermore, I am instructed that the script should return if no solution is found.
Here is my code:
n=100;
A=randn(n);
B=randn(n);
x = A\B;
I believe I know how to solve the equation, but don't know how to return if no solution is found. Is there a different way that I should be writing this? If not, how to I return if no solution is found?

the cyclist

### the cyclist (view profile)

on 13 Sep 2019 at 20:49
Can you be more specific as to what you mean by "no solution"?
Do you mean if
x = A\B;
returns an error message, or something else?

### Walter Roberson (view profile)

on 13 Sep 2019 at 20:55

You can test rank(A) . If it is < n then no solution is possible.
However, there are full rank matrices for which the matrix is too ill-conditioned for an inverse to be calculated. You can example cond() or rcond() and make a decision as to whether the matrix is too badly conditioned to proceed on.

### David Hill (view profile)

on 13 Sep 2019 at 21:05

If A will always be a square matrix, then if the det(A)==0 then return (no solution).

Walter Roberson

### Walter Roberson (view profile)

on 13 Sep 2019 at 21:24
det()==0 is not as good a test as rank() because det() is more prone to round-off error.