(R) → M2 (R) defined by adA (B) = AB − BA is a linear transformation. Find bases for the kernel and the range of adA.
(R) → M2 (R) defined by adA (B) = AB − BA is a linear transformation. Find bases for the kernel and the range of adA.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 16CM
Related questions
Question
For A =
[
1 2
0 1 ]
, show that the mapping adA : M2 (R) → M2 (R) defined by adA (B) =
AB − BA is a linear transformation. Find bases for the kernel and the range of adA.
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