Rank nullity Dimension theorem

which of the following is a vector space?

• Q over R

• R over C

• Q over C

• R over R

• All of the above

• YES

• NO

A singleton set consisting of a non-zero vector is always:

• linearly independent

• linearly dependent

• both of above

• none of above

Every ________of a linearly dependent set of vectors is linearly dependent:

Find the dimension of subspace generated by (0,0,1) and (1,1,1)?

• 3

• 2

• 1

• 0

Let W be a subspace of a finite dimensional vector space V(F), then dim V/W=

• dim V + dim W

• dim V - dim W

• dim V / dim W

• dim V * dim W

• dim (R(T)) + dim(N(T))

• dim (R(T)) - dim(N(T))

• dim (R(T)) * dim(N(T))

• None of them

• Singular

• Non Singular

• Zero Transformation

• None of above

The composition of two Linear Transformation is again a Linear Transformation.

• False

• True