Let v be a vector space of dimension 4. determine if each statement is true or false. (a) any set of 5 vectors in v must be linearly dependent. (b) any set of 5 vectors in v must span v (c) any set of 4 nonzero vectors in v must be a basis for v. (d) any set of 3 vectors in v must be linearly independent (e) no set of 3 vectors in v can span v.

a) True

b) False

c) False

d) False

e) True

Step-by-step explanation:

a) Each basis of V has four vectors. Then any set of 5 vectors must be linear dependent (LD).

b) Suppose that is a basis of V. Considere the set where are scalars. The set has 5 vectors but because is not belong to A and  is linear independent of

c)  Suppose that is a basis of V. Considere the set where are scalars. A has four nonzero vectors but isn't a basis because is a LD set.

d)  Suppose that is a basis of V. Considere the set where are scalars. A has 3 nonzero vectors but isn't a basis because is a LD set.

e)  Since any basis of V must have 4 elements, then a set of three vectors cannot generate V.

step-by-step explanation: