Let V be a finite-dimensional vector space and T : V → V be a linear transformation. (a) Suppose V = R(T) + N(T). Show that V = R(T) ⊕ N(T). (b) Suppose that R(T) ∩ N(T) = {0}. Show that V = R(T) ⊕ N(T).
Let V be a finite-dimensional vector space and T : V → V be a linear transformation. (a) Suppose V = R(T) + N(T). Show that V = R(T) ⊕ N(T). (b) Suppose that R(T) ∩ N(T) = {0}. Show that V = R(T) ⊕ N(T).
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.2: The Kernewl And Range Of A Linear Transformation
Problem 3E: Finding the Kernel of a Linear Transformation In Exercises 1-10, find the kernel of the linear...
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Let V be a finite-dimensional
(a) Suppose V = R(T) + N(T). Show that V = R(T) ⊕ N(T).
(b) Suppose that R(T) ∩ N(T) = {0}. Show that V = R(T) ⊕ N(T).
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