Question 4. Suppose that X = {x₁,x₂,.,x} is a subset Inner Product space. Which option is correct? a. b. C. d. If X = {x₁,x₂,,x} is an orthogonal set so |x₁ + x₂ If X = = {x₁,x₂,,x} is an orthonormal set so 1x₁ + x₂ + ... + x₁₂/1/² Xn = n both none +...+ X₁1 + x₂ 1²³ = |x₁|² + |x₂|² + ···+|x₁|²

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Q: (E, Q4: state and prove L is a normed space ? e a ne. Vila a convex set.

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Q: If ACB then (UNA)U(BNA)=B. TO نقطة واحدة If X = (A, A, = (-1- i,1+i), iEN }, then nA = empty set. F…

A: 1 If A⊆B. Check whether U∩A∪B∩A=B Take LHS  U∩A∪B∩A=A∪B∩A    ∵[A⊆U]=A∪A          ∵[A⊆B]=A The…

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A: Here sets A,B and C are given. We find dim(A),dim(B) and dim(C).

Q: Other Math Yes a = [5 1], b = [1 4], c = [15 3], d = [8 13] Classify each of the following…

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Q: a) Show that the set S = {(1, 2, 3), (0, 1, 2), (– 2, 0, 1)} spans R³. b) Determine whether the set…

A: See the attachment.

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A: NOTE: According to guideline answer of first three related subpart can be given, for other please…

Q: Q. Let X = {a,b,c,d}, T = {o, X, {a}, {b,c,d}}. Then the topological space (X,T) is a. Normal and…

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Q: 1. Let 1 -0-0-0-0 = = = (a) (5 points) Find a orthonormal set {q1, 92, 93, 94} such that span{a₁,…

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Q: Q. Let S = {(x, y), x² + 4y2 = 4} CR2, then S - {point} is homeomorphic to – y? = 4} a. {(x, y), 4x2…

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Q: But change the problem to say A={1,5,7,11}, B={3,5,7}, C={3,7,9,11}

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Q: 6. For A, B, subsets of R, define A+B= {a+b : a € A,b € B} and A·B = {ab : a € A, b E B} (a) For A =…

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Q: 2. (Counting Elements of Finite Sets). Let A, B, C be finite sets. Show that |AU BUC| = |A|+B+C|-|An…

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Q: 3. Suppose that A, B C R2. (a) If A and B are homeomorphic, are A and B homeomorphic? (b) If A and B…

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Q: Let n e N. Suppose An = {n,n +1, n +2,...} and T = {0, An}nɛN• (a) Show that T is a topology on N,…

A: As per the guideline, we are supposed to do the first three subparts of a problem. Kindly repost the…