Which of the following is a subspace of R3 ?

Question

All vectors of the form (a,b,c) where b=c=0

None of these

Answer 1

The set of vectors of the form <a, 0, 0> is a subspace of R³ since the set contains the zero vector, is closed under addition and is closed under scalar multiplication.

The set of vectors of the form <a, 1, 1> is not a subspace of R³ since the zero vector is not in the set.

The set of vectors of the form <a, b, c> where b = a + c + 1 is not a subspace of R³ since the zero vector is not in the set.