Consider the linear space C[0, 1] equipped with the norm ||f || = max |f(t)|. te[0,1] Prove that there is no inner product on C[0, 1] agreed with this norm.

Q: Let U be a subspace of the vector space P100 (R), with dim(U) = 37. Suppose W is another subspace of…

A: P100(R) is a vector space  of all polynomial of degree 100 and smaller. The dimension is 101.For…

Q: Let L : V → W be an isomorphism of vector space V onto vector space W .(a) Prove that L (0V ) = 0W…

A: let V,W be the vectot spces and L be the linear transformation L:V→W , if L be an isomorphism then…

Q: Define a function f : C -> C by f(x+iy) = (x+2y) + i(3x+4y) for x,y in R. Show that f is additive…

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Q: Let V be a real vector space with basis v1, v2 and define a dot product by v1 · v1 = 1, v1 · v2 = v2…

A: (V,•) is real inner product space iff associated matrix A is positive definite.

Q: N 1. Let X := RN be the N-dimensional real vector space with the usual norm, that is, ||x|| := / x²…

A: I have attached the image below Explanation:

Q: Let a: V → V be a projection, where V a 3-dimensional vector space over C, and suppose that the…

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Q: Which of the following subsets is not a vector subspace in the vector space R2[r]?

A: The correct option is:e){ a+bx∣a+b−1=0}Explanation:

Q: 5.2. Prove that if V is a vector space having dimension n, then a system of vectors V1, V2, ..., Vn…

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Q: 3. Let V denote the vector space of all functions f: R" → R, equipped with addition + : V x V → V…

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Q: Consider polynomials with real coefficients and degree at most n. Pn(R)= {ao + a₁x + a₂x²+...+ anxai…

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Q: Find a basis {p(x), g(x)} for the vector space {f(x) = P₂(1) | f'(-2) = f(1)} where P₂(x) is the…

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Q: 3. Let V = P3, the vector space of polynomials of degree at most 3. Let B = {1, t, t, t³} and C =…

A: Part A)- Given: Let V=P3, the vector space of polynomials of degree at most 3. Let B=1,t,t2,t3 be…