Given X = (R, Tstd) and Y = in the subspace topology. (IR, Tstd), draw and write down the set descriptions of the following sets a) B = [0, 0) x (-0, 0], B, Bº, ðB, limit points of B and Ext(B). b) C = {3} × (1, 5), C, C°, aC, limit points of C and Ext(C).

Q: Determine whether the set in P_2 is linearly independent.    S={x^2 , +1, 2 - 1, 2}

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Q: Q2) Let (A,T)be topological spaces; i=1,2,3. Then A, x A2 x Az is homomorphic to (A, x A2) x A3 I

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Q: Q6) Determine whether the set S spans R³. If the set doesn't span R³, give a geometric description…

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Q: Let u = (2, 3, 1), v = (1, 3, 0), and w = (2, -3, 3). Since (1/2)u -(2/3)v - (1/6)w = (0, 0, 0), can…

A: A set of vectors u1, u2, ……, un is said to be linearly independent if c1u1+c2u2+……+cnun=0 implies…

Q: (a) b:a+b+e=2

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Q: b) Evaluate S(2y + 4z)dx + (2æ + 3z)dy + (4x + 3y)dz, where C is the curve given by r(t) = for 0 <t…

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Q: Find two examples for equivalet norms on three dimensional real space R³. .

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Q: Verify that {u₁,u2} is an orthogonal set, and then find the orthogonal projection of y onto…

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Q: The two open disks B((1, 2); 2) and B((-2, 1); 2) has intersection. True False

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Q: Let x = (13, −20, 15), v1 = (1, −2, 3), and v2 = (−1, 1, 1). Then the set {v1, v2} is orthogonal. It…

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Q: Let W1=span{(1,1,0),(-1,1,0)} and W2=span{(1,0,2),(-1,0,4)} Proove W1+W2=R^3

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Q: Consider the vectors u1 = (1, 2, 1), u2 = (0, 3, 2) and u3 = (−2, 1, 1). Determine whether the set S…

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Q: Let X be a nonempty set with subsets, A, B, and C. Prove that A ∩ (B \ C) = (A ∩ B) \ (A ∩ B). I…

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Q: 4={(-21.r):reR} II) B=(2r.-31): te R} III) C={(2r+3,-41) re R} I)

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Q: 2. Determine if the following vectors constitute a linearly independent set.

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Q: Consider the vectors u1 = (1, 2, 1), u2 = (0, 3, 2) and u3 = (−2, 1, 1). Determine whether the set S…

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Q: If (X,7,) and (X,7,) T. - spaces, then (X,7,nt) is also a T,- space. GOOD LUCK

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Q: Suppose that {u, v} is a linearly independent set. Show that the set {u – v, u + v} is also linearly…

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Q: Q) Let A be diagonalizable so that P-1AP = D. Show that A2 must be diagonalizable.

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Q: Let A = {(1, –2,0), (0,0, 1), (-1, 2,0)}. Determine if A spans R. If A does not span R°, give a…

A: To find wheather A spans R3 we have to check if it forms a basis in R3

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