Evaluate the value of I = (4,0). I = Sleby. r 3x) dx + (6xe6y + y)dy, where I is the straight line from (0, 0) to

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Q: Problem 10 The transformation T: P3 → P3 given by T(f(x)) = x f'(x) + x² ƒ"(x) is linear. True False

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Q: 5. Let a, b, c, and n be integers. Prove that if a = b (mod n) and c = d (mod n), then a − c = b -d…

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Q: Write out the negations of the following propositions: (a) (3m) ((m<8) ^ (m ≥ 2)).

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A: Given that Ax=b is consistent and let u1 be a particular solution. That is Au1=b.

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Q: Make a change of variable, x = Py. Give P and the new quadratic form. Q(x) = 4x + 7x² + 4x1x2

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Q: 15. The ratio of the volumes of two similar solids is 1:2. Find the ratio of their surface areas.

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Q: Let A = 36 58 and B = Find -3A+ 3B. -7 7 -84

A: A = 3658 and B =  -77-84 -3A = -3 3658 = -9-18-15-24 3B = 3 -77-84 = -2121-2412

Q: How to show that: If M is a finitely generated R-module and mM = M, then M = 0.

A: How to show that: If M is a finitely generated R-module and mM = M, then M = 0.

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Q: 4. (i) Let v1 = 〈1, 2, 0, 3〉 , v2 = 〈4, 0, 5, 8〉, v3 = 〈8, 1, 5, 6〉 and W a subspace of R4 spanned…

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Q: Find a least-squares solution of the inconsistent system Ax = b, and determine the least-squares…

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Q: 0 0 1 0 0 0 corresponding to the eigenvalue -2? Consider the matrix A = = 0 2 span 0 2 -BB) (10)…

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Q: 2) Solve the following differential equations d²y dy 4. dx² 2d²y 29 dx² a) b) - dx - 45y = 3x² — 1…

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Q: 5- Solve the differential equation y(5) + y = sin(x)

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