4. Let V = R' and let T be the linear operator on V defined by T(1, y, 2, t) = (3t, -y+ 42, 5y, z- 21). a) Let W be the T-cyclic subspace generated by e = (1,0,0,0). Find an ordered basis for W. b) Let U be the T-cyclic subspace generated by eg = (0,0,1,0). Find an ordered basis for U.

4. Let V = R' and let T be the linear operator on V defined by T(1, y, 2, t) = (3t, -y+ 42, 5y, z- 21). a) Let W be the T-cyclic subspace generated by e = (1,0,0,0). Find an ordered basis for W. b) Let U be the T-cyclic subspace generated by eg = (0,0,1,0). Find an ordered basis for U.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.6: The Matrix Of A Linear Transformation

Problem 43EQ

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Question

4.
Let V = R and lot T be the linear operator on V defined by
T(1, y, z, t) = (3t, -y+ 42, 5y, r- 2t).
a) Let W be the T-cyclic subspace generated by e, = (1,0,0,0). Find an ordered basis for W.
b) Let U be the T-cyclic subspace generated by ez = (0,0, 1,0). Find an ordered basis for U.

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