4. Consider the real vector space R?. For every x = (11,12) E R?, let ||x|| = |11|+ |r2l. a) Show that || - || defines a norm on R2. b) Sketch the unit circle {x € R? : ||x| = 1}.

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A: TRUE

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A: Please check the answer in next step

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A:

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A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

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A: Given set A={1,2}

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Q: A subset (a,b) ≤R is T2-space in (R,Tu) * 1 true 2 False

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A: as per our company guideline we are supposed to answer only one qs kindly post remaining qs in next…

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A: Consider the given information.

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Q: Define on R, the metric d defined by d(x, y) = |1+1리 1+ |y| Then (R, d) is not complete. True False

A: Given

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A: ANSWER :

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A: See the detailed solution below.

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A: This is a problem of Functional Analysis.

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