Let M = [4 4 0 -4 4 0 14] 2 1 Find formulas for the entries of M", where n is a positive integer.

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A: We are givenFormula

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Q: Find Euler's equation for the following functional b G[x(t)] = [(x¹². 1= 22x²+x²)dt; x(a) = a, x(b)…

A: The Euler Lagrane equation  of the functional is  .

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Q: A Let T be the linear transformation of P2(F) defined by the formula T(P(x)) = (x+2) P'(x) - P(x) a)…

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Q: Given the function f(x,y) = 4y-2x, answer the following questions. a. Find the function's domain. b.…

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Q: B: Suppose T(x, y, z) = (3x − 6y +3z, x+y+z, −x). a) Use the matrix M = M(T) to compute T2(x, y, z).

A: Given linear transformation is .Now the standard basis for vector space  is .Now  So we have Now

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Q: Given the function f(x,y) = 4y - 6x, answer the following questions. a. Find the function's domain.…

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Q: Fill in the blank. The symbols C₁, C₂, and k represent constants. d² dx² (C₁ cos kx + C₂2 sin kx) =…

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Q: Solve the differential equation z²y" - 3xy' +3y=0 with initial condition y(0) = 2, y'(0) = 2.

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Q: Given two bases B = {(−1, −1,2), (−1, −2,3), (1, −6, 6)} V1 V2 U1 and C = {(1, −1, −1), (−1, −1,1),…

A: Given two bases  and of .(i) Find the change of coordinates (transition) matrix  from the…