I'm trying to finish these linear independence proofs:

3. Let S = {v1, v2, v3} be a linearly independent subset of V and let

T = {v1 + v2, v2 + v3, v1 + v3}.

(a) Show that if char F is not 2, then T is linearly independent.

(b) Show that if char F = 2, then T is not linearly independent.

4. Show that if a subset S of V is linearly independent, then any nonempty subset T of S

is also linearly independent.

5. Show that if a subset S of V is linearly independent and v ∈ V is not in sp(S), then

S ∪ {v} is linearly independent

3. linear independent so a1v1+a2v2+a3v3=0 implies a1=a2=a3=0

The characteristic is confusing me

Like I want to say we have something like 1+1+....+1=0

4.linear independent so a1v1+a2v2+a3v3=0 implies a1=a2=a3=0

I know we want a1(v1+v2)+a2(v2+v3)+a3(v1+v3)=0 to imply a1=a2=a3=0

we have a1v1+a1v2+a2v2+a2v3+a3v1+a3v3=0

(a1v1+a2v2+a3v3)+a1v2+a2v3+a3v1=0

a1v2+a2v3+a3v1=0

5.linear independent so a1v1+a2v2+a3v3=0 implies a1=a2=a3=0

v is not in sp(s), so not a linear combination

so v is not in a1v1+a2v2+a3v3

Any hints would be greatly appreciated