Find all scalars c, if any exist such that the given statement is true. vector [13, -15] is a linear combination of the vectors [1, 5] and [3, c]

Question

Find all scalars c, if any exist such that the given statement is true.  vector [13, -15] is a linear combination of the vectors [1, 5] and [3, c]

anonymous · Answer

If the vectors (1,5) and (3,c) are linearly independent, then they will span all of the plane.  So (13,-15) would have to be some linear combination of them. 

So basically, this question is asking you to find the values of c so that the vectors (1,5) and (3,c) are linear independent.