Prove Equationally that F A → B → A.

Q: Show that the operator U is positive U: 1² ([0,1]) → L²([0,1]), Uƒ (x) = X[{0,1] [~*\f(t)\dt

A: To show that the operator U is positive, need to demonstrate that for any f∈L2([0,1]), the inner…

Q: Evaluate the commutators of the operators (a) d/dx and 1/x, (b)d/dx and x2.

A: Given:  a)  ddx and 1x b) ddxand x2 To Find: Commutator of the operators

Q: Verify that (AB)T = BTAT.

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Q: Prove that S3 = Inn(S3) = Aut(S3).

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Q: b) Find the work done along AB A(1,-1, 2) F=5i + 3j + 2k B(3, 2, -4)

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Q: Evaluate |(a,b)=(0,0) given that f(x, y) = 3x² + [y]; x = e²a+b₁ e²a+b; y = a² + t² + 1 да

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Q: equational-style proof to prove the theorem schema + (B+C) = (((Bv C) → C)) = (((BAC) V T)) (3) Use…

A: Let's prove the given theorem schema using equational-style proof. Want to show:1. Prove :   Will…

Q: dx Show that f - In|ax + b| + C where a # 0. ax+b

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Q: Let f(x) = v3x + 4, let g(x) = Va, and let u = 3x + 4. Thus, f(x) = g(u) Part 1 Part 2 Part 3

A: Follow next step

Q: Prove BCスツ+)B[スかリック =B(X1y)

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Q: Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies.…

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Q: If z = 1 - 2j and w= 2 - 3j, express 2. w in the form a + bj where a and b are real.

A: Given  z=1−2jw=2−3j

Q: dw 22. If w = f(ax + by), show that b = 0. a ду Hint: Let ax + by = z.

A: Consider the following equation: z=ax+by Differentiate z with respect to x taking y as constant:…

Q: | (4z + 4y + 4+8zy) dA where R= [1,2] x (0,1]. R Let I Find

A: Given: ∬4x+4y+4+8xyddwhereR=1,2x0,11

Q: Prove that (X+Y) (X+Z) =X+YZ

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Q: 2 11 Q2) Assume A = |1 3 [3 2 4 1 and B = show that (AB)' = B' A' %3D 3 6 4J 4]

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Q: Let A = x x² 1 I 2 I T² T³ 1 1 8 1 x x² Find a such that det (A) = 0.

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Q: Calculate az/ax, where xez + zeY = x + y.

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Q: Show that Alf・g) = (Adig + 2D fo@g+ f(Ag)

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