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Mark only correct statements. a. There is a nilpotent matrix with eigenvalue one. O b. The following matrix 100 001 000 is in the Jordan form. k c. There is a square matrix which is not similar to its transpose over complex field.

Mark only correct statements. a. There is a nilpotent matrix with eigenvalue one. O b. The following matrix 100 001 000 is in the Jordan form. k c. There is a square matrix which is not similar to its transpose over complex field.

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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please list only correct statements. please pay all your attention to the image that I attached. please try to solve this problem as fast as possible! thank you

Mark only correct statements. a. There is a nilpotent matrix with eigenvalue one. O b. The following matrix 100 001 000 is in the Jordan form. k c. There is a square matrix which is not similar to its transpose over complex field. Od. If T' is a linear operator on a finite-dimensional vector space V and A € C, then the space of all generalized eigenvectors for A and the zero vector equals the null space of the operator (T-AI)dim V v, Av, A²v, ..., Akv are linearly dependent. □e. If A is a nilpotent matrix such that Akv 0 for some integer k and some vectore v, then the vectors
Transcribed Image Text:Mark only correct statements. a. There is a nilpotent matrix with eigenvalue one. O b. The following matrix 100 001 000 is in the Jordan form. k c. There is a square matrix which is not similar to its transpose over complex field. Od. If T' is a linear operator on a finite-dimensional vector space V and A € C, then the space of all generalized eigenvectors for A and the zero vector equals the null space of the operator (T-AI)dim V v, Av, A²v, ..., Akv are linearly dependent. □e. If A is a nilpotent matrix such that Akv 0 for some integer k and some vectore v, then the vectors
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