a)Give an example (with proof) of a square matrix with nonzero numbers along the diagonal which is not invertible. b)Give an example of a linear operator T : V →V and F = R so that for any basis B, the matrix M(T; B) is not upper-triangular(with proof)
a)Give an example (with proof) of a square matrix with nonzero numbers along the diagonal which is not invertible. b)Give an example of a linear operator T : V →V and F = R so that for any basis B, the matrix M(T; B) is not upper-triangular(with proof)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section: Chapter Questions
Problem 17RQ
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a)Give an example (with proof) of a square matrix with nonzero numbers
along the diagonal which is not invertible.
b)Give an example of a linear operator T : V →V and F = R so that for
any basis B, the matrix M(T; B) is not upper-triangular(with proof)
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sorry, I do not think part b is correct,can you try to use eignvector and basis to proof the matrix is not upper-triangular?
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