et q1, ..., qn be a set of independent generalized coordinates for a system of n degrees of freedom, with a Lagrangian L(q, q˙, t). Suppose we transform to another set of independent coordinates s1, s2, ..., sn by means of transformation equations qi = qi(s1, ..., sn, t), i = 1, ..., n Show that if the Lagrangian function is expressed as a function of sj, s˙j, and t through the equations of transformation, then L satisfies Lagrange’s

Q: Let be the linear transformation defined L. Find L

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Q: Let , üz = 7, i = -2 and w %3D Let R'+ R be the linear transformation satisfying T() = w1, T(2) =…

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Q: Be= (2, –1,0), u2 = (1,0, 1), Uz = (0, –4, 1), vi = (0, 2, 1), v2 = (2,3, 4)andU3 = (1,1, 1). %3D…

A: Given vectors are: u1=2,-1,0, u2=1,0,1, u3=0,-4,1 and v1=0,2,1, v2=2,3,4, v3=1,1,1. Given linear…

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Q: assume thatf (2, 3) = 8, fx (2, 3) = 5, fy (2, 3) = 7 Which of (a)–(b) is the linearization of f at…

A: Consider the given: f2,3=8fx2,3=5,fy2,3=7,

Q: Find the Jacobian of following functions f(x,y,z) = 3xy – yz + 2y³z² – 5xyz³ g(x,y, z) = xyz – x³yz…

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Q: 4-Find the coordinates the front trace F for line AB, if A(2, 1, -2) and B(3, 3, -5). * O (1,-1) O…

A: A=(2,1,-2) B=(3,3,-5)

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Q: 1.6 Describe the transformation and write down the rule used in the form (x; y). ..

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Q: 2 - 1 Fit a cubic trend function to the data (- 2,11), (- 1,13), (0,13), (1,12), (2,11). Let po(t) =…

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Q: 36. Let T be a linear transformation from R² to R². Let ₁, 2, and be three vectors in R2, as shown…

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Q: Let T : F" → F" be the linear transformation sending the vector (x1,..., xn) to (xn, X1, x2, . .. ,…

A: Given T:Fn→Fn be the linear transformation such that Tx1,x2,.....,xn=xn,x1,x2,.....,xn-1…

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Q: Let a = (d1, d2, a3, d4) where Let T: R4 → R4 be a linear transformation given by T(ते) = 31, T(dे०)…

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Q: 1. (15) Consider the transformation T(f) = 2f' - f", where f has at least first two derivatives.…

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Q: 4. (a) Are the points u = independent? (1, 2, 3), v = (-1,0, 1) and w = (5, 4, 3) linearly (b) If…

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Q: 8. Decide which of the following sets are linearly independent in Rn. Justify your answer in each…

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Q: Find the Jacobian of transformation J

A: For calculating the Jacobian of a transformation the formula is given by - J = ∂x,y∂r,θ =…

Q: Task 17 Let a, 3 > 0 I(a) := / 1"-e" dr, B(a, 8) := (1 - p)-'p-1 dp. Show that : r(a)I(3) = r(a+ B)…

A: Given: Γα=∫0∞xα-1e-xdx, B(α, β)=∫011-pα-1pβ-1dp, where α, β>0. To show: Γ(α) Γ(β)=Γ(α+β) B(α, β)