# Matrix with an Unknown

## Main Question or Discussion Point

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

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Homework Helper
What is the relation between the system determinant and the uniqueness of the solution?

I am not sure...I thought the system determinant is only used to find the interdependency of the basis. If there exist such a relation as you have mentioned....that is not mentioned in the question; so we can assume anything for the problem.

By the way in order to have a unique solution r(A), rank equals n. But we know n but I don't know how to get rank!

Notice how if b = 3 then column 4 becomes a multible of column 1. This solution would make the rank(C) < n = 4 and therfore C would not have an inverse making the system have no unique solitions.

Thanks Live2Learn.......I got it!!!