please give me detailed solution

1. (a) A set {v1, ..vk} is said to be lineary independent if all vi 6= 0 and
ifa1vi1 + ..apvip = 0 implies ai = 0 for all i. Then we say set is
linearly independent.
(b) T : Rn → Rk is called linear transformation if for any α, β ∈ R, and
v, w ∈ Rn, we have
T (av + bw) = aT (v) + bT (w)
(c) We say set {v1, ..vk} forms a basis for a vector space V if set is linearly
independent and any element v ∈ V can be written as
v =
k∑
i=1
αivi
for some αi ∈ R.
(d) W is called a subspace...