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gtfitzpatrick
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Homework Statement
T = {(1,1,1),(0,0,1)} is a subset of R[tex]^{3}[/tex] but not a subspace
sol
i have to prove it holds for addition and scalar multiplication
so let x=(1,1,1) and y =(0,0,1) so x+y = (1,1,2)
so it holds
let [tex]\alpha[/tex] = a scalar
then [tex]\alpha[/tex]x = ([tex]\alpha[/tex],[tex]\alpha[/tex],[tex]\alpha[/tex])
and [tex]\alpha[/tex]y = (0,0,[tex]\alpha[/tex])
so that holds.
i think I've shown that it is a subpace but the question says it isnt?
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