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.
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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