be the vector spaces consisting of zero and polynomials in z of degree <3 and degree < 6 respectively. This question concerns the map a: V → W which sends a polynomial f(r) in V to f(2²) in W. (a) Show that a is linear as a map V → W.

Q: (4) Suppose V and W are finite dimensional vector spaces such that dim(V) > dim(W). Show that any…

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Q: For a polynomial p ao + a₁x + a₂x² + + anx, let p denote the polynomial obtained from p by removing…

A: Note:  As you requested only Part C(I) so I answered here only that.

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Q: 3) Let V be a vector space and denote Vk: := V × ... × V as the cartesian product of itself k times.…

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Q: Let V be the set of all pairs (x,y) of real numbers together with the following operations: (x1,y1)…

A: Given  be the set of all pairs  of real numbers together with the following operations:

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Q: Let u and v be nonzero orthogonal vectors in R3. Find bases for the range space and null space of…

A: To find: To find the bases for the range space and null space using the given function f: ℝ3→ℝ3,…

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Q: Consider the vector space V = P over the field of real numbers F = R. Is the vector 4 – x – x 2 in…

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Q: Let V = R' and define vector addition as (x, y, z)+(x', y', z')= (x+x',y+y',z+z') (standard…

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Q: Define T : R? → R by 7((x, y)) = x+y. Describe the kernel of and fibers of T geometrically.

A: The kernel is a line with slope -1 and passes through the origin.

Q: Let V be a vector space and suppose there exist maps S, T = L(V, V) such that range(S) ℃ null(T).…

A: Let V be a vector space and suppose there exist maps S,T:V→V such that .We need to prove that the…

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A: According to our guidelines we can answer only one question and rest can be reposted.