Let v1→=[23] and v1→=[46] what is the **span** of the vector space defined by v1→ and v1→? Explain your answer in detail?

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Gordon Stephens · Accepted Answer

span ({v1→,v2→})={λv1→∣λ∈F}  Explanation: Typically we talk about the span of a set of vectors, rather than of an entire vector space. We will proceed, then, in examining the span of {v1→,v2→} within a given vector space.  The span of a set of vectors in a vector space is the set of all finite linear combinations of those vectors. That is, given a subset S of a vector space over a field F, we have  span(S)={∑i=1kλksk∣n∈N,si∈S,λi∈F}  (the set of any finite sum with each term being the product of a scalar and an element of S)  For simplicity, we will assume that our given vector space is over some subfield F of C. Then, applying the above definition:  span({v1→,v2→})={∑i=1kλivi∣λi∈F}    ={λ1v1→+λ2v2→∣λ1,λ2∈F}  But note that v2→=2v1→, and so, for any λ1,λ2∈F  λ1v1→+λ2v2→=λ1v1→+λ2(2v1→)=(λ1+2λ2)v1→  Then, as any linear combination of {v1→andv2→} can be expressed as a scalar multiple of {v1→, and any scalar multiple of {v1→ can be expressed as a linear combination of {v1→andv2→} by setting λ2=0 we have  ({v1→,v2→})={λv1→∣λ∈F}

Let vec(v_1)=[[2],[3]] and vec(v_1)=[[4],[6]] what is the span of the

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