Let M be a n x real matrix such that det (M): = 0. Then which of the following is/are true? Select all possible answers. All the eigenvalues of M are non-zero. There should exist an eigenvector of M with eigenvalue 0. There exists another n x neal matrix N such that MN = NM = In The dimension of the rowspace of M equals n The dimension of the columnspace of Mequals n The nullspace of M has dimension at least 1 The system of linear equation: Ma Onust have a unique solution.
Let M be a n x real matrix such that det (M): = 0. Then which of the following is/are true? Select all possible answers. All the eigenvalues of M are non-zero. There should exist an eigenvector of M with eigenvalue 0. There exists another n x neal matrix N such that MN = NM = In The dimension of the rowspace of M equals n The dimension of the columnspace of Mequals n The nullspace of M has dimension at least 1 The system of linear equation: Ma Onust have a unique solution.
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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Transcribed Image Text:Let M be a n x nreal matrix such that det (M):
= 0. Then which of the following is/are true?
Select all possible answers.
All the eigenvalues of M are non-zero.
| There should exist an eigenvector of M with eigenvalue 0.
There exists another n x neal matrix N such that MN = NM = In
The dimension of the rowspace of M equals n
The dimension of the columnspace of M equals n
The nullspace of M has dimension at least 1
The system of linear equation: Ma
Onust have a unique solution.
O O
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