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Let V be the vector space of all 3 × 3 matrices with real entries, and consider the linear transformation T : V → V given by T(X) = AX + XA, where 1 1 0 02 0 A = 00-1 Compute the determinant det T.

Let V be the vector space of all 3 × 3 matrices with real entries, and consider the linear transformation T : V → V given by T(X) = AX + XA, where 1 1 0 02 0 A = 00-1 Compute the determinant det T.

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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Let V be the vector space of all 3 x 3 matrices with real entries, and consider the linear transformation T: V → V given by T(X) = AX + XA, where 1 1 0 A = -(69) 02 0 00- Compute the determinant det T.
Transcribed Image Text:Let V be the vector space of all 3 x 3 matrices with real entries, and consider the linear transformation T: V → V given by T(X) = AX + XA, where 1 1 0 A = -(69) 02 0 00- Compute the determinant det T.
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