Solved: Sum of Two Linear Transformations In Exercises 67
Chapter 6, Problem 68(choose chapter or problem)
In Exercises 67 and 68, consider the sum S + T of two linear transformations \(S: V \rightarrow W\) and \(T: V \rightarrow W\), defined as (S + T)(v) = S(v) + T(v).
Give an example for each.
(a) Rank(S + T) = rank(S) + rank(T)
(b) Rank(S + T) < rank(S) + rank(T)
Text Transcription:
S: V rightarrow W
T: V rightarrow W
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