Show that T is a linear transformation by finding a matrix that implements the mapping. Note that X₁, X2₁. are not vectors but are entries in a vector. T(X₁ X2 X3 X4) = 4x₁ + 2x₂ + 3x3 + x4 (T: R¹→R) A =

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A: The nth term of an arithmetic sequence is: an=72-n-1. To Do:(a) Find the first five terms of the…

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A: The solution is given by

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Q: a) (A) = AU b) (An B)⁰ = Aºn Bº c) A° U B°C (AUB)⁰

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Q: 4. Prove that 473 1 (3n+1)³ 81√3

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A: The datasets for Model A and Model B are given as-Model AModel BSample sizeSample meanSample…

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A: sample size(n)=417 x=152 confidence level=95% sample proportion(p^)=xn=152417≅0.365

Q: Suppose that f(x, y) is a smooth function and that its partial derivatives have the values, fz(-1,…

A: Given that, f(-1,-3)=-4; fx(-1,-3)=-5 and fy(-1,-3)=3. Now find the following:

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A: I have explained everything with in the solution. Please go through that.

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A: Here we have to write x as sum of span {u1, u2, u3 } and span {u4}.

Q: Use the simplex method to solve the linear programming problem. z = 7x₁ +4x₂ + x3 5x₁ +5x2 + x3 ≤ 15…

A: Let us solve the given problem by simplex method.

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Q: The null and alternate hypotheses are: He: Ha so H1 Hd>0 The following sample information shows the…

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A: If there exists the same proportional change between the independent variables, then the variables…

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Q: b) Use Ferrari's method to derive all the roots of the equation x² + 25 = 26x².

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Q: The 1990 census reported that 40% of the households in Middletown were homeowners and the remainder…

A: Given,  The 1990 census reported that 40% of the households in Middletown were homeowners and the…

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Q: Two functions g and fare defined in the figure below.

A: Note that from the given information g(8) = 2 , but f is not defined at 2. i.e f(2) is undefined So…

Q: 2. Which of the following differential equation is exact? (Show your work) a. (sin x + y)dx + (3y -…

A: The differential equation Mdx+Ndy=0 is exact differential equation if ∂M∂y=∂N∂x.

Q: Suppose that (a)=1 is a sequence and n Σa converges to 12. Let sn= Σak. n=1 k = 1 Which of the…

A: Sequence  converges to 12 and Let To Find:Which of the following option is correct:a) b) Divergence…

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Q: . Find a particular solution to the inhomogeneous equation y" – 9y/ + 8y = e* in the form y(r) = c-…

A: To find A particular solution to the inhomogeneous equation in the form y(x) =Ce^(2x)

Q: Write a description of the shaded region using the symbols A, B, C, u, N, -, and ' as needed. (A…

A: (A (top left) Shaded) (C (bottom middle) shaded) (B (top right) Unshaded) (background unshaded)

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A: Here Given  Evens are  (I) Drawing a card of red four or  Drawing a card of red ten

Q: Let B = {b₁,b₂} and C = {C₁,C₂} be bases for R². Find the change-of-coordinates matrix from B to C…

A: B = < b1 , b2 >  C = < c1 , c2 >  We see,         b1 = (-1, 1)T = 3(1, 3)T - 4(1, 2)T…

Q: So Use the transition matrix P shown to find S₁ and S₂ for the initial-state matrix S₁ = [0.7 0.3].…

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Q: 2. Solve dy dx = e 5x + sin 3x + 2x; y(0) = 2

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Q: Find a matrix P such that PTAP orthogonally diagonalizes A. Verify that PTAP gives the proper…

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Q: You are a newsvendor selling the San Pedro Times every morning. Before you get to work, you go to…

A: Cost price of paper=$0.35 per copySelling price of paper=$1.35 per copyDemand meanμ=305S.Dσ=61

Q: Diagonalize A 13 - [22] 42 O a. A = PDP-1 A = 3 50 P-[71] - [82] Р D 4 O b. A = PDP-1 ----[9] -4 1 P…

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