Show that translations are commutative. That is, if matrix T(d) represents a translation by d₂ translation by d, and matrix T(d₂) represents then T(d, ) T(d2₂) = T (d₂)T(d₂). "

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Q: 1. Use Gauss elimination method to solve the linear system -1 1 x1 F436-0 1 -1 x2 = -1 X3 32

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A: According to guidelines we can do only first three sub parts thank youUse the angle sum relationship…

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A: Note: According to the guidelines we are allowed to solve three subpart at a time. Please post rest…

Q: Objective Function Subject To Kmax.= y₁ + 2y2 Y₁ + y₂ ≤ 0.7 Y₁-Y2 ≥ Log2 0≤y₁ ≤1 0≤y₂ ≤1 y ≥0…

A: Objective function subjected to

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Q: Let S := a + √2 b + √2 : a, b EN Prove that S is countably infinite.

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Q: Solve the system of linear equations Using the Cramer's Rule. E A) 182 B 8x+6y=1 Sx - 2y = -37 D 691…

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Q: 8. d²y dy Solve the Cauchy-Euler equation x²- +8x +6y=0. dx² dx

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Q: the differential equation that describes the motion.

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A: Birkhoff's Ergodic Theorem states that for almost every point x in our space and for any integrable…

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Q: (a)Suppose that f is an injection. Show that f -1∘f(x) = x for all x∊D(f) and that f∘f -1(y)=y for…

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Q: 1. Show that the following functions are convex by verifying the definition, i.e., that f(x +…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

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Q: 1. Consider the following function, sin 1(2) - (2²46² (²) ƒ(x): if x = 0 if x = 0 Prove that the…

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Q: B. Express the ff atticher whit with general Form quadortic function. 1. 2 9=C++3) ²-3 FLAMU

A: The general form of a quadratic function is

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Q: Determine the number of permutations (arrangements) possible of 7 things taken 3 at a time.

A: We have to determine the number of possible permutations of 7 things taken  at a time.So,

Q: 4. (i) For an odd number n, suppose that 2" # 2 mod n. Can n be a prime? Explain. This is called the…

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Q: and if f(x) = sin" (x²) Lim 0 find 2m + n f(x) f'(x) (1 − cos x)m - = 2√√√3

A: Given that                                                            Formula:…

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Q: 3. 4. sin n √n √√n² + 2 n² + n-n

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Q: A club N with four members is shown below. N = {Aaron, Brad, Cindy, Dennis), abbreviated as N = {A,…

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Q: . Find the Fourier transform of the unit gate function |1| 121|2

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Q: Find a basis B for the span of the given vectors. 8 HAD 0 1 8 -1 0 0 2 -2

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Q: 12. Let xo < x < < x, and let f be continuously differentiable. Show that a f[xo, x₁, x₂] = f[xo,…

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Q: & (in/in) fps (ksi) 0.01 230 0.02 255 0.03 260 0.04 264 0.05 268 0.058 270

A: Given information:To find: when .Concept used:The concept of interpolation will be used to estimate…

Q: Find the least-squares line given the matrix products ATA 608.4 5942.2 A¹b- = y = Ex: 1.2 +Ex: 1.2 €…

A: Let us to find a least square line for the set of values {(xi,yi):i=1,2,⋯,n}Let the equation of line…

Q: 10+ 8 6 4 2 -6 -5 -4 3 -2 -1 -2 -4 -6 -8 -10+ 1 2 3 4 5 6 The function graphed above is: Concave up…

A: A point of inflection of the graph of a function f is a point where the second derivative…