Let S= {a, a ,a_} be an orthonormal set of vectors in an inner product space V(F). If a vector B in V is in the linear span of S then prove that B=E (B, a) a. k=1

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A: By definition: A sequence xn in a Hilbert space H is a frame if there exist numbers A, B>0such…

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A: (a) Given vectors are u1^→=1,0,0,1,u2^→=1,1,0,0,u3^→=0,0,1,1.   Consider U^=spanu1^→, u2^→, u3^→.…

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Q: find the Linear trans fromation Tee whose matrix Wzxz i -1 Hi- + =1421] -2 with regard to the base H…

A: Question had typo. Hence solved after correction

Q: Let {u1, u2, u3} be an orthonormal basis for an innerproduct space V. If x = c1u1 + c2u2 + c3u3 isa…

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Q: 2. Let V and W be vector spaces and let TE L(V, W). (a) Suppose V is finite-dimesnional, m is a…

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A: Given , is an inner product on vector space V over real numbers. Therefore for all u,v,w∈Vand a∈ℝ:…

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A: In order to find the explicit description of NulA we have to find the solution of the system Ax=0…

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Q: Let (,) be an inner product in the vector space V. Given an isomorphismT : U + V. Score [u, v] =…

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Q: Determine

A: Length of all vectors is 1.

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Q: 7. Let S = Show that span S = R and find a basis for R' consisting of vectors from S. %3D

A: The solution is given as

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Q: Let {u1, u2, u2} be an orthonormal basis for an inner product space V. Suppose v = au1 + buz + cu3…

A: Topic:- vector algebra

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Q: = 15. Define the vector space spanned by v₁ = (2.1.3) and v₂ 16. Show that the set (1,3,5).

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A: See the attachment

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A: Let's find.

Q: Let V be a space with an inner product. Show that if w is orthogonal to each of the vectors v1, V2,…

A: Let V be a space with an inner product. Show that if w is orthogonal to each of the vectors v1, v2,…

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Q: 3. Why zero vector space has no independent subset?

A: detailed solution given below on given statement