# Consider the set ? = ((x, x+ y, 2y)|x,y are real) of vectors in r3 . Is W a subspace? If yes, prove it and if no explain the reason.

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Consider the set ? = ((x, x+ y, 2y)|x,y are real) of vectors in r3 . Is W a subspace? If yes, prove it and if no explain the reason.

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Step 1

We have Set S = {(x, x + y, 2y) | x, y are real}. Let u, v be any two element of S then,

Step 2

Let a and b be any two element of R. In order to prove that S is a subspace of V, we have to prove that au + bv S, for which we have to show that au + bv is expressible in the form ... help_outlineImage Transcriptionclosea(xxy2)+ b(x,.x, +y,2y,) - aι+bν - (α + bx ) (α + bx) +(ωγ +by ) 2 (α + bv) au+ bν ( α,α + β, 2β) where α- a, + bx, and βa) +bν, Φau + bν au+bν E S fullscreen

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