Q4Multiple correct6 Marks26 Oct 2025Choose all the correct statements from the following.AThe set of positive real numbers is a vector subspace of R\mathbb{R}R with the standard addition and multiplication.BIn any vector space VVV, if for some c∈Rc\in\mathbb{R}c∈R and v∈Vv\in Vv∈V, we have c⋅v=0c\cdot v=0c⋅v=0, then c=0c=0c=0 or vvv is the zero vector.CIf a vector subspace of R3\mathbb{R}^3R3 with usual addition and scalar multiplication contains finitely many elements, then it is the trivial subspace, i.e., the subspace with only the zero vector.DAny subset of a spanning set of a vector space is a spanning set.EAny subset of a linearly independent set in a vector space is a linearly independent set.
