Is the linear Diophantine equation solvable? If yes, give all the solutions; If not, why? (a) 36x +102y = 8 (b) 6x + 4y = 42

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A: It is ''slope is not defined at corner points ".

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A: Solved using basic properties of elementary number theory.

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Q: Use Euler's Formula to prove the following identities: Cos 0 = е' eie te 2 -i0 and sin = eie-eie 2i

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Q: 3. Let f: RS be a ring homomorphism (a) If I is an ideal of S, prove the pre-image of I, that is…

A: Let I be an ideal of a ring R , and Let f:R→S be a ring homomorphism.  To prove: f-1I is an ideal of…

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Q: Can you give the Prismoidal Formula of Cube, Rectangular Prism, Pyramid, Cylinder, Cone, Sphere?

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Q: Problem 5. Find all linear operators T: R4 → R4 such that SOT TOS for every linear operator S: R4 →…

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Q: Given A = -5-2 -9-3-2 2 1 6 0 } x = and b Solve the maxtrix equation Ax = b for x 150 100 400

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Q: 20. If a € Z and a = 1 (mod 5), then a² = 1 (mod 5). 23. Let a, b, c € Z and n EN. If a = b (mod n),…

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A: The system of functions given is as follows: f1x, y=lnx+y+sinxy-2=0f2x, y=0.52x+3y+logx=0 The…

Q: xy² + y = y ²³

A: Given : xy'+y=1y3 To Find : Solution of Given differential equation . Note : According to the…

Q: 6. Let I be an ideal of a ring R and let : R→→ R/I be the canonical homomorphism (a) =a+I. Define :…

A: We shall solve each step in great details, please check the next steps

Q: Given the following matrices A and B, find an elementary matrix E such that B = EA: You can resize a…

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Q: (a) The curve with equation 2 y 3 + y2 - y 5   = x 4 -2x3  +x 2  has been likened to a bouncing…

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Q: 3. Find the domain of (f + g)(x) when f(x) = x-3 and g(x) = 4 x+2

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Q: Let V be a vector space with dim(V) = n. Consider V₁, V2, ..., um € V. Which of the following is/are…

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Q: 4. Find the volume of the solid generated by rotating the region bounded by curve x = -y² + y and…

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Q: Consider the following Gauss elimination: [100] [1 0 07 A 0 0 1 A 0 1 0 E₁A → 0 1 0 E₂E₁A → 0-1 0…

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Q: 1. Consider the equation (2¹ +64) = 32√√3³. Find all the roots and express them in rectangular form.…

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Q: 1. Find the double integral ſf xy²dA where D is the region enclosed by the lines x = 1, y = 0 and y…

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Q: 6 + 5 4 3 f(x) 2 1 2 -1 f(2) + g(3) f(2) g(1) - ma -3 4 LO 5 X 6 VENDED 8 g(x) 0 1 2 g(1) - f(0)…

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Q: Find a polynomial f(x) of degree ≤ 6 with integer coefficients such that for every integer n, we…

A: Using Euler Totient theorem.

Q: m-1 1 If * Σ( ² ) = 4( ¹ - ₂ = ²/₁ ) ₁ ₁ k=1 2m m «£ () simplification of 04(1-2-²-1) 2m 04 (1+ 1 2m…

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Q: An excercise: Find all the left cosets of in S4

A: We have been given S4, a symmetric group. We have to find all the left cosets of <1 2 3 4>in…