Which of the following are subspaces of the vector space of n n matrices M nn

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Which of the following are subspaces of the vector space of n × n matrices Mn×n? The set of all 

(a) Regular matrices; 

(b) Nonsingular matrices; 

(c) Singular matrices;
(d) Lower triangular matrices; 

(e) Lower unitriangular matrices; 

(f) Diagonal matrices;
(g) Symmetric matrices; 

(h) Skew-symmetric matrices.

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Applied Linear Algebra

ISBN: 9783319910406

2nd Edition

Authors: Peter J. Olver, Chehrzad Shakiban

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