Question: need correction options, with reason, Only, QUESTION 5 Let V be the set of all 3x3 matrices with Real number entries, with the usual definitions

need correction options, with reason, Only,

QUESTION 5 Let V be the set of all 3x3 matrices with Real number entries, with the usual definitions of scalar multiplication and vector addition. Consider whether V is a vector space over C. Mark all true statements (there may be more than on]). O a. V is a vector space over C O b. The additive closure axiom is not satisfied O c. The scalar closure axiom is satisfied O d. The additive inverse axiom is not satisfied e. The zero axiom is satisfied Of. V is not a vector space over C O g. The additive inverse axiom is satisfied O h. The zero axiom is not satisfied O) i. The scalar closure axiom is not satisfiedQUESTION 6 Let V be the set of all 2x2 matrices with Complex number entries, with the usual definitions of scalar multiplication and vector addition. Consider whether V is a vector space over R. Mark all true statements (there may be more than one). O a. The scalar closure axiom is satisfied O b. V is a vector space over R O c. The zero axiom is satisfied O d. The additive closure axiom is satsified O e. The scalar closure axiom is not satisfied O f. The additive closure axiom is not satisfied O g. The zero axiom is not satisfied O h. The additive inverse axiom is satisfied O i. V is not a vector space over O j. The additive inverse axiom is not satisfiedQUESTION 9 Let / be the set of second degree polynomials H = {ax? + bx: a,b EC} Is H a subspace of P2 ? Why or why not? Select all correct answer choices (there may be more than one). O a. H is not a subspace of P2 because it is not closed under vector addition O b. H is a subspace of P2 because it contains only second degree polynomials O c. H is a subspace of P2 because it contains the zero vector of P2 d. H is a subspace of P2 because it can be written as the span of a subset of P2 O e. H is not a subspace of P2 because it is not closed under scalar multiplication O f. H is not a subspace of P2 because it does not contain the zero vector of P2 me. H is a subspace of Po because it is closed under vector addition and scalar multiplication

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