Let A = 2 1 54 Write 5A. Is det(5A) equal to 5det(A)? 5A= (Type an integer or decimal for each matrix element.) ………

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A: Two matrices A and B  are similar if there exist an invertible matrix P such that B=P-1AP

Q: (A) F; has an open graph. (B) F; is lower (C) D₁ = {a € A | F;(a) # 0} is open in A. hemicontinuous.

A: note : Since you have posted question with multiple sub parts, we will provide the solution only to…

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Q: (c) Prove that f(n) → f(a) and f(yng) → f(a) as k→∞, and conclude the proof of Theorem I

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A: The given function is, ft=t sinat. Laplace transform is, Lft=∫0∞e-stftdt. Integration by parts is,…

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A: We recall some basics facts about Euler's function to solve this problem.

Q: 15. Assume A and B are unitary matrices (A) The determinant of A can be -1 (B) (AB)T= A-¹B-1 (C) A…

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Q: Find the solution of the given initial value problem. 2x²y" — 5xy' — 9y = 0, y(1) = 1, y′(1) = 10…

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Q: 22. If {1, e2x, xe2} is a basis of solutions of y"" + ay" +by' + cy = 0, Chen b = (a) 2 (b) -2 -4…

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Q: 1. 2xy® + 1 + (3x?yf - y1) dy dx = 0

A: 2xy3+1+3x2y2-y-1dydx=0 Note: According to the guidelines we are allowed to solve one question at a…

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A: Yes, it is possible to take a walk around the city whose map is given, starting and ending at the…

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Q: (b) [MTH3140. Students in MTH2140 will assume it to be true.] Prove that f is non-decreasing.…

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Q: 5. (a) Use Stokes' theorem to calculate the circulation of the vector field F around the curve C.…

A: Stokes theorem:

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A: Given  surface  is x=y+2z² , 0<=y<=1,0<=z<=3 . To evaluate the given surface integral,…

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A: The flux of the vector field F across the surface S is the surface integral over the surface S .

Q: Answer 3(b)

A: note : As per the instructions we will only solve the part (b) of the question.

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A: To decode this using the RSA cryptosystem.

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A: First we assume the fraction as x/y, then follow the given assumption in question.

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A: Definitions: Euler trail is a path in a finite graph that visits every edge exactly once…

Q: Weekly Exercise Let C be the segment consisting of the segments from (0, 2) to (0, 0), and from (0,…

A: Given  fz = z + 2                     where  z  =  x + iy   ⇒ dz = dx + i dy…

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Q: nan (x - 3)n-1 + x Σ an (ax - 3)* = 0, + n=0 then the recurrence relation can be written as Q6. If Σ…

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Q: which predicts the weight from the rest of the data. Find the best approximation of this function,…

A: As per the question we are given a data table relating height h, age a, gender g with weight w And…

Q: (e) y" — 8k²x²y = 0, x = 0, k constant - (f) (1 − x)y" + 8y = 0, x₁ = 0 (g) y" + 8xy' + 18y = 0, x =…

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Q: A periodic function is defined by f(t) = {2t₂ - 1≤t<0, f(t+2) = f(t). Let F(t) be the Fourier series…

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Q: Question 14 1 2 3 4 The above two graphs are isomorphic. O True O False C d b a

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Q: Q4. If W (1, x, f(x)) = 9e³2 and f(0) = 1, (a) e³-3x (b) 2e-3-1 (c) e-3 +31 f'(0) = 0, then f(x) =…

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Q: (i) Let G be a group. If : Zx Z→G is a homomorphism $(1,0) = h while Þ(0, 1) = k, find (m, n).

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Q: 10. Convert 333 to a base five number. A. 2312FIVE B. 2313 FIVE 11. Convert 55 to a base two number.…

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