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# Linear Algebra Help watch

1. 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)
2. (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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