Solve the matrix equation AX = B for X. 3 1 34 *)-1] B= 42 5 6 X = A =

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A: To Solve: The following LP: Maximize $4x + $5y Subject to            4x + 5y ≤ 72…

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Q: For each of the following functions f(x) (x € R²), describe the sets = { x | f(x) ≤ 4} and show, by…

A: As per guidelines, I can only first three subparts of the question ( parts (a), (b), (c))

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A: We use induction method.

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Q: . Show that the following set is convex: with A € Sn C₁ = {x = R" x Ax ≤ 1},

A: Let x,y∈Rn. Then  (x-y)TA(x-y):=<A(x-y),x-y>≥0, where <.,.> is the usual inner product…

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A: Given,         3s(s2+8)(s-2).

Q: Homogeneous Systems Produce the basis vectors for all non-trivial solutions 3x + 2y + 4z + w = 0 1x…

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Q: tan¹ (2x) x sin(3x4 + 8x³) f(x) = { [ / (x + ¹)] 1) cot-¹ cosh (³+-+1)). if x 1

A: fx=tan42xxsin3x4+8x3if x<012x+1if 0≤x≤1cot-1cosh3x+11-xif x>1 At x=0 For continuity…

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Q: 2. (yexy - 2y³)dx + (xexy - 6xy² - 2y)dy = 0; when y(0) = 2

A: Let us consider the differential equation Mdx+Ndy=0. Then the equation is exact if ∂M∂y=∂N∂x. Then…

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Q: 3. Find the solution of the DE 2yy" = 1 + (y')², x > 0, y > 0.

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Q: a) log, 6 b) log, 3

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Q: Let F(x) = f(f(x)) and G(x) = (F(x))². You also know that f(5) = 9, f(9) = 2, f'(9) = 4, f'(5) = 6…

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Q: number of solutions, express them in terms of the - 8 -2 18 X X X = y = Z = - 2x + Y + 2z 6z 4y - =

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Q: 3. Prove that for all m, n, and p, we have the equality (mn) - p = m (n+p). [Hint: Prove that for…

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Q: 1 [²2² +0 Compute the approximation MID(3) for the integral x²+x+1dx

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