-8-B- 1. Let T be the linear transformation of Rª to Rª that takes and and takes and |2 a) Explain why there is one and only one linear transformation from R* to R* that does this. b) Find bases for both the kernel and the range of this linear transformation. c) Give an orthonormal basis for the kernel of this transformation. d) Indicate the matrix that would represent T with respect to the standard basis for R*.

-8-B- 1. Let T be the linear transformation of Rª to Rª that takes and and takes and |2 a) Explain why there is one and only one linear transformation from R* to R* that does this. b) Find bases for both the kernel and the range of this linear transformation. c) Give an orthonormal basis for the kernel of this transformation. d) Indicate the matrix that would represent T with respect to the standard basis for R*.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A: See the detailed solution below.

Question

1. Let T be the linear transformation of Rª to Rª that takes
1
and
and
and takes
a) Explain why there is one and only one linear transformation from Rª to Rª that does this.
b) Find bases for both the kernel and the range of this linear transformation.
c) Give an orthonormal basis for the kernel of this transformation.
d) Indicate the matrix that would represent T with respect to the standard basis for R*.

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