Let S = {v1, v2, v3, v4} be a set of four vectors in R3, and let T: R3 - R4 be a linear transformation?
T or F: S cannot be linearly independent in R3
T or F: S must span R3
T or F: It must be possible to write v4 as a linear combination of {v1, v2, v3}
T or F: T must be a one-to-one function.

I figured out the other true or false ones, but I haven't been able to get these ones yet. Any help? Thanks!

Question

Let S = {v1, v2, v3, v4} be a set of four vectors in R3, and let T: R3 -> R4 be a linear transformation?
T or F: S cannot be linearly independent in R3
T or F: S must span R3
T or F: It must be possible to write v4 as a linear combination of {v1, v2, v3}
T or F: T must be a one-to-one function.

I figured out the other true or false ones, but I haven't been able to get these ones yet. Any help? Thanks!