4. a. Solve the system u = 2x – 3y, v = -x + y for x and y in terms of u and v. Then find the value of the Jacobian a(x, y)/Ə(u, v). b. Find the image under the transformation u = 2x – 3y, v = -x + y of the parallelogram R in the xy-plane with boundaries x = -3, x = 0, y = x, and y = x + 1. Sketch the transformed region in the uv-plane.

4. a. Solve the system u = 2x – 3y, v = -x + y for x and y in terms of u and v. Then find the value of the Jacobian a(x, y)/Ə(u, v). b. Find the image under the transformation u = 2x – 3y, v = -x + y of the parallelogram R in the xy-plane with boundaries x = -3, x = 0, y = x, and y = x + 1. Sketch the transformed region in the uv-plane.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 12EQ

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