**Unformatted text preview: **2 . #4. Let x any y be vectors in R k . Show that y is uniquely represented in the form y = a + b, where a,b ∈ R k satisfy a = αx for some real α, and b · x = 0 . Verify this fact for x = (1 , 1 , 1) and y = (1 , 2 , 3) in R 3 . #5. Let A be a nonempty set in R k . Deﬁne d ( x ) := inf {| x-a | : a ∈ A } . Show that | d ( x )-d ( y ) | ≤ | x-y | for all x,y ∈ R k ....

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