2 Let T: R³ R³ be the linear transformation determined 0 b where a, b, and c are 0 a by the matrix A = 0 0 0 0 C positive numbers. Let S be the unit ball, whose bounding surface has the equation x + x + x3 = 1. a. Show that T(S) is bounded by the ellipsoid with the equation + + = 1. b. Use the fact that the volume of the unit ball is 47/3 to determine the volume of the region bounded by the ellipsoid in part (a).

2 Let T: R³ R³ be the linear transformation determined 0 b where a, b, and c are 0 a by the matrix A = 0 0 0 0 C positive numbers. Let S be the unit ball, whose bounding surface has the equation x + x + x3 = 1. a. Show that T(S) is bounded by the ellipsoid with the equation + + = 1. b. Use the fact that the volume of the unit ball is 47/3 to determine the volume of the region bounded by the ellipsoid in part (a).

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 17CM

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