If a set contains p vectors in Rn and p n then the set is l

If a set contains p vectors in R^n and p > n, then the set is linearly dependent. If a set of vectors contains the zero vector, then the set is linearly dependent. If a set contains exactly one vector and it is nonzero, then the set is linearly independent. A set of vectors in linearly dependent if and only if at least one vector in the set can be written as a linear combination of other vectors in the set.

Solution

(b)

True.

Since Rn has dimension n so a set can have at most n linearly independent vectors.

(c)

True.

Because then we can write

1*0+0*(a+b+c+....)=0

where, a,b,c are other vectors in the set

(d)

True.

Let, x be the vector

Since there are no other vectors so x cannot be written as linear combination of any other vectors hence set is linearly independent by definition

(e)

True.

This is the definition of linear dependence of set of vectors.