Problem 5. Let U, V, W be finite dimensional vector spaces over F. Show that for all TEL(U, V) and S = L(V, W), 1. dim(ker ST) ≤ dim(ker S) + dim(ker T).
Problem 5. Let U, V, W be finite dimensional vector spaces over F. Show that for all TEL(U, V) and S = L(V, W), 1. dim(ker ST) ≤ dim(ker S) + dim(ker T).
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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Transcribed Image Text:Problem 5. Let U, V, W be finite dimensional vector spaces over F. Show that for all
T = L(U, V) and S = L(V, W),
1.
dim(ker ST) ≤ dim(ker S) + dim(ker T).
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