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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Pls solve this question correctly instantly in 5 min i will give u 3 like for sure
![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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbf4e9f68-b5eb-4a27-ae76-fd0a8c3d58af%2F0e22e55b-9e2c-44ac-a1ee-1bb3a5142063%2Fi6vffq_processed.jpeg&w=3840&q=75)
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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