If x = v'u and y = 2uv, show that JJ' - 1, where J is the jacobian of u,v with respect to x and y and ' is the jacobian of x, y with respect to u and v.

Q: Calculate û x ô if û = ĵ + 2k and û = -i - ĵ + k. %3D

A: Topic = Vector   if u→ =a1i+a2j+a3k and v→ =b1i+b2j+b3kthenu→×v→=ijka1a2a3b1b2b3

Q: Solve the differential equation by variation of parameters. 1 2 + ex y" + 3y + 2y =

A: The given differential equation is y''+3y'+2y=12+ex. The objective is to solve the differential…

Q: Transform the equation: 2x2y'' + xy' + 3y = 0 to the form of: a(d2y/dz2) + b(dy/dz) + cy = 0 (a,…

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Q: Let X and Y be random variables. Suppose P(X=0, Y = 0) = .1, P(X= 1, Y = 0) = .3, P(X= 2, Y = 0) = 2…

A: For the given joint probability distribution of x and Y, we need to find the covariance of X and Y.…

Q: Consider the simple lincar model Y, = Be + B,x, + C. where -N(0,0²); i= 1,2, --,n. 1. Show that a)…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts(a, b-i,…

Q: ?w Əv у Find when u = 0, v=0 if w=x² + ₁ x=6u-2v + 1₁ y=u+4v - 1.

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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: Show that U(−f, p) = −L(f, p) and L(−f, p) = −U(f,p)

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Q: Calculate fz(3, 6, 9), where f(x, y, z) = xyz. fz(3, 6, 9) =

A:

Q: Show that Cov(aX+b,cY+d)=acCov(X,Y)

A: We Know that, Covariance between any two random variables is given by,  Cov(T,Z)= E(TZ)-E(T)*E(Z)…

Q: If u = (u, uz) and v = (V1, V2), how do you find u + v?

A: Given: u=(u1,u2)v=(v1,v2)

Q: 4) Find the adjoint of the operator Lu = u" + 4u'- 3u, where u'(0) = -4u(0), u(1) = -4u(1).

A: The objective is to find the adjoint of the operator, Lu=u''+4u'-3u where u'(0)=-4u(0), u'(1)=-4u(1)…

Q: If Fu,y, z) = xzi + xyzj =ý k, find v.È %3D ........

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Q: d) Let g(x,y) = (3x + y)2(2y + 1) and h(x, y) = 6y2(2x + y) h i) Find дх’ ду’ дх’ ду

A: The given functions are  and

Q: H012.3.4,53 Find sets CandD such that A= CBUC)\ D.

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Q: Evaluate S(z² + 3z)dz along the straight line from (2,0) to (2, 2) and then from (2, 2) to (0, 2).

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Q: use implici't differen tiatiom to brind dyldu at the pont (2,2) = 1+y" エ+Scu

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Q: Q1. If the components of a contravariant vector in (x') coordinate system are (3,4). Find its…

A: 1) Given information: x¯1 = 7x1 - 5x2x¯2 = -5x1 + 4x2 The components of contravariant in xi…

Q: Let x' = (1, 1, 3) and y' = (-2, 0, -2). calculate the angle between x and y

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Q: linearise R = AT + BT

A: To linearise the below equation. R=AT+BT2

Q: Show that t, e^t, and sin(t) are linearly independent.

A: In the given question we have to show that t, e^t, and sin(t) are linearly independent.

Q: a(x,y) d(u,v) Evaluate the Jacobian for the change of variables X =, =u²cos(v) and y =usin (v).

A: Topic : calculus

Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)

Q: Find Cov(X, Y)

A: Covariance: It is a statistical measure used to establish a relationship between two random…

Q: Verify the chain rule for jacobian, if y2 u = x + , v = * y2 %3D

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.