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

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Answered: (a) If ker(L) has dimension s, what is…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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(a) If ker(L) has dimension 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.