Let T : R^7 to R^4 be a linear transformation and v1,v2,v3 be linearly dependent. Prove that T(v1), T(v2), T(v3) are linearly dependent in R^4.
Give an Example of a non zero linear transformation S : R^3 to R^3 and an example of three linearly independent vectors v1,v2,v3 in R^3 such that the vectors S(v1), S(v2), S(v3) are linearly dependent.
Totally lost on this. I get the basic idea of a linear transformation but have no idea how to prove the Above. Any easy methods?