(a) Every set of four linearly independent vectorsin R4is a basisof R4. (b) Ever

Question

(a) Every set of four linearly independent vectorsin R4is a basisof R4.

(b) Every set of linearly independent vectorsin R4is a basis ofsome subspace of R4.

(c) If W =Span{v1; v2; v3}, then{v1; v2; v3}must be abasis of W.

(d) If R3 =Span{v1; v2; v3}, then{v1; v2; v3}must be abasis of R3.

(e) No set of five vectors inR4is a basisof R4.

(f) No set of four vectors inR5can span asubspace of dimension 3.

(g) Suppose W =Span{v1; v2; v3}is a subspaceof dimension 2. Then {v1; v2}is a basisof W.

Explanation / Answer

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