Mark the statements below that must be true
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This is a homework question and I was wondering what would you do to determine if a statement is true. I have already solved the first part of the question
$w = 2x-4y $
I have a screenshot with two of the choices as I want to solve the rest by myself. I know that the span is the set consisting of all linear combinations of some vectors but I am completely lost about what to do next.
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$\begingroup$The point is that z is a linear combination of x and y and then calculating w= 2x- 4y shows that w is also a linear combination of x and y. We can replace z in Span(y,z) with a linear combination of x and y so, yes, Span(y,z)= Span(x,y). Similarly we can replace w in Span(w,y) with a linear combination of x and y so Span(w,y)= Span(x,y)= Span(y,z)= Span(x,y,z).
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