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2) Let V and W be vector spaces, let T : V B = = {V₁, V₂, ..., Un} be a basis of V, and let C be a basis of W. (a) Prove that ker(T) ≈ Null(c[T]3) by constructing an explicit isomorphism. (b) Prove that nullity (T) = nullity (c[T]B). W be a linear transformation, let

2) Let V and W be vector spaces, let T : V B = = {V₁, V₂, ..., Un} be a basis of V, and let C be a basis of W. (a) Prove that ker(T) ≈ Null(c[T]3) by constructing an explicit isomorphism. (b) Prove that nullity (T) = nullity (c[T]B). W be a linear transformation, let

Advanced Engineering Mathematics
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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2) Let V and W be vector spaces, let T : V → W be a linear transformation, let B = {V1, V2, ..., n} be a basis of V, and let C be a basis of W. (a) Prove that ker(T) ≈ Null(c[T]B) by constructing an explicit isomorphism. (b) Prove that nullity (T) = nullity (c[T]B).
Transcribed Image Text:2) Let V and W be vector spaces, let T : V → W be a linear transformation, let B = {V1, V2, ..., n} be a basis of V, and let C be a basis of W. (a) Prove that ker(T) ≈ Null(c[T]B) by constructing an explicit isomorphism. (b) Prove that nullity (T) = nullity (c[T]B).
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