3. The region Ris bounded by the lines y = 2x+1, y = 2x+3, y= 5-x and y = 3-x. Calculatethe Jacobian transformation by using an appropriate transformation u and v. Hence, evaluateS[ -xy- 2x*) dA.4. Find the volume of the tetrahedron bounded by the plane 2x+ y+z= 2 and the three coordinateplanes.(0,0,2)2x+y+z = 2(0.2.0)(1,0,0)

Answered: Image /qna-images/answer/5c9d3f4b-8ee9-4f1f-96a1-86b0dbaf48fb.jpg

Answered: 3. The region Ris bounded by the lines…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 3CM: Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions...

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Similar questions

Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).
Find a basis B for R3 such that the matrix for the linear transformation T:R3R3, T(x,y,z)=(2x2z,2y2z,3x3z), relative to B is diagonal.
Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions of Rn and Rm.
Suppose S is a rectangle in the uv plane with vertices O(0,0), P(delta u, 0), (delta u, delta v), Q(0, delta v). The image of S under the transformation x=g(u,v), y=h(u,v) is a region R in the xy plane. Let O', P' and Q' be the images of O,P,Q, respectively, in the xy plane where O',P',Q' do not all lie on the same line. The coordinates of O' , P', and Q' are (g(0,0),h(0,0)), (g(delta u,0),h(delta u,0)), and (g(0,delta v),h(0,delta v)), respectively. Consider the parallelogram determined by the vectors O'P' and O'Q'. Use the cross product to show that the area of the parallelogram is approximately |J(u,v)|delta(u)delta(v). |J(u,v)| is the jacobian determinant.
Consider the region RR in the xyxy-plane that is described by the intersection of the four lines: 2x−1y=2 2x−1y=5 3x+5y=3 3x+5y=5 Use the transformation T described by u=2x−1y and v=3x+5y to evaluate the following double integral: ∬R (2x−1y) sqrt(3x+5y) dx dy
What is the rank of linear transformation T from R3 to R3 defined by T(x,y,z)=(y,0,z)
Let R be the region bounded by the lines x − 2y = 0, x − 2y = −4, x + y = 4, and x + y = 1 . Find a transformation T from a region S to R such that S is a rectangular region (with sides parallel to the u- or v-axis).
Find the Jacobian ∂(x, y, z)/∂(u, y, w) of the transformation x = 2u - 1, y = 3v - 4, z = (1/2)(w - 4).
let T(x,y) = (2x-y, xy) a) What is T(0,0) ? b) Is T a linear transformation? Explain c) Find the image under T of the region R bounded y=1/x ; y=2/x ; y= 2x; y=2x-1 d) ∫∫ R ( 2x+y/xy)dA where R is the same as in part (c)
Let S = {z: 1 =< Re(z) =< 2 & 1 =< Im(z)}. Find the image of transformed region w-plane under bi-linear transformation of f (z) = (z + 1)/(z – 1). (Hint: Note that a semi-line, a line segment or a circular arc can be transformed to a semi-line, line segment or a circular arc under bi- linear transformation. A line is specified completely, if two point on line is determined, while a circle is specified completely if three distinct points are determined.)
Given (picture attached)f (x, y) dx dy and the transformation x = u/v and y = uv with u > 0 and v > 0 a) To translate the integral to the uv coordinate system, find the Jacobian determinant. b) In the uv coodinate system, find the boundaries of the altered region and sketch it. For the points of intersection, make sure to include labels and values. You'll notice that there are three borders to consider.
a. Solve the system u = 3x + 2y, y = x + 4y for x and y in terms of u and y. Then find the value of the Jacobian ∂(x, y)/∂(u, y). b. Find the image under the transformation u = 3x + 2y, y = x + 4y of the triangular region in the xy-plane bounded by the x-axis, the y-axis, and the line x + y = 1. Sketch the transformed region in the uy-plane.

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