Question

Suppose that T is a one-to-one transformation, so that an equation T(u)=T(v) always implies u=v. Show that if the set of images {T(v_1),....,T(v_p)} is linearly dependent, then {v_1,.....v_p} is linearly dependent

Answer 1

If you assume that the the set:\[(v_1,v_2,\ldots, v_p)\]is not linearly independent, you should be able to force a contradiction in the fact that \[T(v_1),T(v_2),\ldots, T(v_p)\] is linearly independent.