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Linear Transformations in an Arbitrary Basis Let TV V be a linear operator, and let S be a (finite) basis of V. Let VEV be a vector. Prove that [T(v)]s = = [T]s([v]s) Hint: Represent the vectors [v] and [T(v)]s using the basis S, and use linearity of the operator applied to [v]s to obtain equality.

Linear Transformations in an Arbitrary Basis Let TV V be a linear operator, and let S be a (finite) basis of V. Let VEV be a vector. Prove that [T(v)]s = = [T]s([v]s) Hint: Represent the vectors [v] and [T(v)]s using the basis S, and use linearity of the operator applied to [v]s to obtain equality.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.5: Basis And Dimension
Problem 69E: Find a basis for R2 that includes the vector (2,2).
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Linear Transformations in an Arbitrary Basis Let TV V be a linear operator, and let S be a (finite) basis of V. Let VEV be a vector. Prove that [T(v)]s = = [T]s([v]s) Hint: Represent the vectors [v] and [T(v)]s using the basis S, and use linearity of the operator applied to [v]s to obtain equality.
Transcribed Image Text:Linear Transformations in an Arbitrary Basis Let TV V be a linear operator, and let S be a (finite) basis of V. Let VEV be a vector. Prove that [T(v)]s = = [T]s([v]s) Hint: Represent the vectors [v] and [T(v)]s using the basis S, and use linearity of the operator applied to [v]s to obtain equality.
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