please prove these

Problem 1. Recall that a function L : R* – Rquot; is (by definition) said to be a linear transformation
if and only if it satisfies L(+ y) = L() + L(y) and L(ri) = rL(i) for every i, ye R* and every r E R.
(a) Prove that a function L : R* – R. is a linear transformation if and only if for every choice of
scalars a, bE R and of vectors , y ( R*, it is the case that L(as + by) = al() + bL(y).
(b) Suppose that L : R* – Rm and T : R* – Rm are two linear transformations such that
L(e:) = T(e;) for all i 6 {1, …, k}. Prove that L = T; that is, prove that L(U) = T(v) for all
JERK
Math