Let U be the set of all vectors (x1, x2, x3) satisfying 3x1 (x1, x2, x3) satisfying 2x₁ − x2 + x3 = 0. x2 + x3 = 0 and V be the set of all vectors (a) Show that U and V are subspaces of R³. (b) Is the set U UV := = {x | x € U or x € V} a subspace of R³? Justify your answer. (c) Is the set Unv := = {x | x € U and x € V} a subspace of R³? Justify your answer.

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A: (.)  Let set  'S'  is given by ,        S=x1,x2,x3∈ℝ3  :  x1=3x2 or   S= x1,x2,x3∈ℝ3 :  x1-3x2=0…

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A: This is a problem of vector calculus.

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A: We now solve this questions

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A: The given vectors .The aim is to find the norm of the vector .