Let M , be the space of all nxn matrices with standard operations. Determine which of the following subsets of M,m are subspaces: (a) The set of all nxn matrices with zero determinant; (b) The set of all symmetric nxn matrices; (c) The set of all nxn matrices such that A" =. -A.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
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Let M.
be the
space
of all
nxn matrices with standard operations. Determine which
nn
of the following subsets of M , are subspaces:
(a) The set of all nxn matrices with zero determinant;
(b) The set of all symmetric nxn matrices;
(c) The set of all nxn matrices such that A' =-A.
Transcribed Image Text:Let M. be the space of all nxn matrices with standard operations. Determine which nn of the following subsets of M , are subspaces: (a) The set of all nxn matrices with zero determinant; (b) The set of all symmetric nxn matrices; (c) The set of all nxn matrices such that A' =-A.
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