2. Let y : V → W be a linear map of vector spaces. (Recall, this means that p(u + v) = p(u) + p(v) and p(.v) = A · p(v) for all A E F and u, v E V.) Prove that p(0v) = 0w where Oy is the zero vector in V and Ow is the zero vector in W.

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Q: What is the dimension of the vector space S=abc detEM2x3(R): a=b=c=0}

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Q: Let f(x) = sin x and  g(x) = sin x + cos x  in the vector space C, [0, 2π] with the inner product…

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Q: Let, T:R' → R;T(x, y, z) = (x + y+ z,2y + z,2 y+3z) verify that [T][v]s = [T (v)]; for any vector v…

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Q: Determine whether or not F(x,y) = (xy + y²,x² + 2xy) is a conservative vector field.

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Q: In any vector space V, show that (a + b)(x + y) = ax + ay + bx + by for any x, y e V and any a, be…

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Q: Recall that for any two given real vector spaces V and W, a function T:V → W is linear if T(ax+by) =…

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Q: Consider the vector field i = P(x, y) = –3y+ ¤(x² + y² – 1), ý = Q(x, y) = 3x +y(x² + y² – 1) | %3D

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Q: Let V be a vector space, and let T: V →V be linear. Prove that T2 = T0 if and only if R(T) ⊆ N(T).

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Q: (ii) Prove that W is a vector space of R°.

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Q: Let V be a finite-dimensional vector space, and let T: V →V be linear. (a) If rank(T) = rank(T2),…

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Q: On a vector space W of all continuous functions from R to R, define I, : W – W as I[f(t))= J', f(7)d…

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Q: the function T:C+C defined by T(2) = z a linear transformation ?What if we consider C as a vector…

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Q: Which one of the following vector fields is conservative? O F(x, Y, z) = (xy +1, a²y? – 2, xyz)…

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Q: 19. Consider the vector field V(x, y, z) = ( HÓ-DE) 1-y x²+(y–1)² » 2+(y-1)2 and the curves 8 : 2 +…

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