20. Suppose TV → W is a linear transformation. a) Show that if v is a vector in V and u is a vector in ker(7), then T (u + v) = T(v). b) Show that if u and v are vectors in V such that T(u) = T(v), then u - v is in ker(T).
20. Suppose TV → W is a linear transformation. a) Show that if v is a vector in V and u is a vector in ker(7), then T (u + v) = T(v). b) Show that if u and v are vectors in V such that T(u) = T(v), then u - v is in 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:20. Suppose T : V → W is a linear transformation.
a) Show that if v is a vector in V and u is a vector
in ker(T), then T(u + v) = T(v).
b) Show that if u and v are vectors in V such that
T(u) = T (v), then u - v is in ker(T).
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