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    Just stuck on a few questions from my uni course, I understand the general idea of them just not sure if I'm getting these ones correct.

    1) W = { x = (x1,x2,x3) | x1x3 >= 0 }

    I'm just unsure if this is a subspace of W, I know that if x1x3 > 0 then it doesn't contain the zero vector so isn't a subspace, but I'm unsure if it is a subspace if it is >= 0? And then if it is a subspace how do I prove it is using z=ax+by?

    2) (x, y) |--> T(x,y) = (x+y , y , x)

    For this I've to characterise the image of T and find the dimension. I know how to work out the dimension, but for the imagine I'm a bit shaky on this stuff... I got Im(T) = {x[1,0,1] + y[1,1,0)} but I'm unsure on that...

    Thanks for any help! (Sorry TSR format has changed since I last used it and couldn't do latex)
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    (Original post by Blue7195)
    Just stuck on a few questions from my uni course, I understand the general idea of them just not sure if I'm getting these ones correct.

    1) W = { x = (x1,x2,x3) | x1x3 >= 0 }

    I'm just unsure if this is a subspace of W, I know that if x1x3 > 0 then it doesn't contain the zero vector so isn't a subspace, but I'm unsure if it is a subspace if it is >= 0? And then if it is a subspace how do I prove it is using z=ax+by?

    2) (x, y) |--> T(x,y) = (x+y , y , x)

    For this I've to characterise the image of T and find the dimension. I know how to work out the dimension, but for the imagine I'm a bit shaky on this stuff... I got Im(T) = {x[1,0,1] + y[1,1,0)} but I'm unsure on that...

    Thanks for any help! (Sorry TSR format has changed since I last used it and couldn't do latex)
    1: does it look like a subspace? Is it closed?
    2: do the dimension first. What dimension did you get? Your image is correct, but you haven't really "characterised" it, in my view: simply restated its definition. I imagine they're looking for an answer of the form "line through the origin and (-1,1,5)".
 
 
 
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