ar Transformations y (7) + rank (T) = dim (V) in this case, namely,
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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Please do only 2(d).
Transcribed Image Text:(2) Let V denote the vector space C² with scalar multiplication over the real numbers R. Define TV → V by
T (x, y) = (x − x, y-y), where (x, y) = V = C²
(a) Show that T is a linear transformation over R.
(b) Find a basis for N (T).
(c) Find a basis for R (T).
(d) Verify the Dimension Theorem for Linear Transformations in this case, namely,
nullity (T) + rank (T) = dim (V)
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