(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let V be a vector over a field F.

a.) Let x1,...,xn∈V and y1,...,ym∈V. Show that

Span(x1,...,xn,y1,...,ym) = Span(x1,...,xn) + Span(y1,...,ym)

B.) Let x1, x2, x3, x4 be four linearly independent vectors in V. Show hat

Span(x1, x2,x3) ∩ Span(x2, x3, x4) = Span(x2,x3)

c.) Show that the equality in part b.) does not hold if we drop the assumption that x1, x2, x3, x4 are linearly independent.

2. Relevant equations

3. The attempt at a solution

I have done a and b just not sure about c:

If x1=x2=x3=x4 and For a ∈ in R,

Span(x1, x2,x3) ∩ Span(x2, x3, x4)= (a1x1+a2x2+a3x3) ∩ (a2x2+a3x3+a4x4)=a1x1+a2x2+a3x3+a4x4= Span(x1, x2, x3, x4)≠ Span(x2,x3)

Is this okay?

or is it ok to just do a counter example using vectors,

if so could somebody show me an example counter example

thanks in advance

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# Homework Help: Vector Spans

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