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 R = {(x,y): |x| + |y| ≤ 2}. Use the transformation x=u+v, y=u-v to evaluate ∫∫ ((x^2)*(e^y))dA

A: Consider the given: R=x,y:x+y≤2x=u+vy=u−vA=111−1=−1−1=−2=2

Q: 4. Let T: R" → Rm be a linear transformation and suppose T(u) = v. Show that T(-u) = -v.

A: Since T is a linear transformation, for any scalar number c, we must have,        T(cu) = cT(u)

Q: Are the following functions are linear transformations? Explain why or why not. a) L : M2×2(R) → R,…

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Q: (3) Consider the linear map T : R? → R? which sends (1,0) (-3,5) and (0, 1) → (4, – 1). (f) Deduce…

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Q: Suppose T is a linear transformation, where ū (1, 0, 0) V = = W = (0, 1, 0) (0, 0, 1) Find the…

A: Solve the following

Q: plesssss

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Q: lai k AGHI is shown in the coordinate plane. 100 Type here to search G Which transformation will…

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Q: True / False. The function L: C'(R) - C(R) defined by L (f) = -f' is a linear transformation.

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Q: explain history of Marshall olkin transformation only why they develop and when it is first use and…

A: The Marshall-Olkin transformation is method to deal with the skewed data modelling or the data which…

Q: let T. R²₁ R² Such that T(x, y) = (2x + y²₁ y=x), Show That Tis linear Transformation.

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Q: Determine the kernel and the range of the linear operator on L(x) = (x1 + x3, X2, 0)

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Q: Explain how to compute the Jacobian of the transformationT: x = g(u, v), y = h(u, v).

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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) =…

A: Given, The data                           -2, 11, -1, 13, 0, 13, 1, 12, 2, 11 and the t-coordinate…

Q: Let L : R^2 → R^2 be a linear transformation. If L((1, 2)^T) = (2, −3)T and L((1, −1)^T) = (5, 2)^T,…

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Q: 5. Let B = {b₁,b2}, where b₁ = √(1,3), b2 = √(-3,1). (a) Specify the transition matrices Ps,B and…

A: The given vectors are b1=1101,3, b2=110-3,1. The given line is y=3x.

Q: Jacobian of the transformation. x = 8v + 8w2, y = 5w + 5u2, z = 3u + 3v z) II

A: We have to solve the given problem

Q: Show that T: R² → R4 is a linear transformation, where T is given by 2x2 3x1 4x2 T ((:))-[***] = X2…

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Q: Let T: R³ → R² be a linear transformation. If it is known that Img (T) = CL {(_^), (8)}, t then…

A: Given  T:R^3 to R^2.    ....(1) And img(T)=CL{(4,-4),8,-8)} ...(2) By (1), T is 2*3 matrix  As we…

Q: T(xy)=Cax?+by?, cx²+dy²) 2

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Q: How is the Jacobian formulated?

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Q: Draw a transformation diagram for v = (3/5)c, with the numbers 1, 2, and 3 (in meters) on the…

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Q: lf T : R³ → R³ is a linear transformation such that then T (D) *(6) - B· ·(D)-A· ^(8) - A (8)-4). T…

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Q: 3. Each of J, K, L, M and N is a linear transformation from R2 to R. These functions are given as…

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Q: If L: R² R³ be defined by L(x, y) = (x, y, 1), show that it is a linear transformation.

A: Introduction: A linear transformation is a function from one vector space to another that respects…

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: Define the linear transformation 7: R^ → Rm by T(v) = Av. Find the dimensions of Rª and Rm. A = 4 1…

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Q: 1 (2¹) 4 4

A: Given matrix as, A=-2144

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)