Originally Posted by

**MrJank** Determine if each of the following are true or false, and give a justification.

(a) Let v_{1}, v_{2} and v_{3} be vectors in a subspace in V. If { v_{1}, v_{2}} is a spanning set of V, then {v_{1}, v_{2,}v_{3}} must be a spanning set of V.

On this one I put true because v_{3} could be a linear combination of v_{1}, v_{2. }(b) Let v_{1}, v_{2,}v_{3 } be vectors in subspace V. If {v_{1}, v_{2,}v_{3}} is a spanning set of V, then { v_{1}, v_{2}} must be a spanning set of V.

Here I put false because if {v_{1}, v_{2,}v_{3}} is linearly dependent, then a vector can't be removed from the set.

(c) Every spanning set of **R**^{2} must contain at least two vectors.

Here I put false but I don't really know why.. I know if I have an image of a matrix [-s,s]^T then the spanning set would only be a single vector [-1,1]^T...Am I on the right track for any of these?