1. Suppose that L : V → W is a linear transforma- tion and that dim(V) = n. (a) If ker(L) has dimensiom s, what is the rank of L? (b) If ker(L) # {0v}, show that L is not invert- ible. (c) For m > 1, find an example of vector spaces V and W and L: V → W a linear transfor- mation such that ker(L) has dimension m.

1. Suppose that L : V → W is a linear transforma- tion and that dim(V) = n. (a) If ker(L) has dimensiom s, what is the rank of L? (b) If ker(L) # {0v}, show that L is not invert- ible. (c) For m > 1, find an example of vector spaces V and W and L: V → W a linear transfor- mation such that ker(L) has dimension m.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 34EQ

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