Matrix Problem with an Unknown quantity

[blackbear]

I have the following matrix, C =

3 2 1 9
4 2 6 12
1 4 -3 3
0 1 8 (3-b)

y1=[-1 -1 1 -1] transpose

For the vector y, I need to find all values of b such that the system of equations y=Cx has no unique solutions. Can someone help...

Thanks

 

[CompuChip]

Perhaps the easiest approach is a "calculational" one... Suppose that a value for b was given. Then how would you go about solving y = Cx. At what point would you be able to tell if there was a unique solution?

 

[blackbear]

I do the problems mostly with mathlab. Anyway, when rank r(A) equals n then there exist a unique solution. But I don't know how to find r(A)!