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fasterthanjoao
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I'm preparing for an end of year linear algebra test which briefly covers things about subsets of Matnxn and their relations to subspaces of Matnxn; I found the following question:
Which of the following subsets of Matn×n are subspaces of Matn×n?
(i) Symmetric matrices (i.e. matrices A such that AT = A).
(ii) Skew-symmetric matrices (i.e. matrices A such that AT = −A).
(iii) Orthogonal matrices (i.e. matrices A such that AT = A−1).
(iv) Singular matrices.
(v) Invertible matrices.
(vi) Echelon matrices.
(vii) Reduced echelon matrices.
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I'd appreciate some guidance on how to tell which of the above apply.. is it the same as showing that vectors in a subset are subspaces when they're closed under addition and linear multiplication?
thanks.
Which of the following subsets of Matn×n are subspaces of Matn×n?
(i) Symmetric matrices (i.e. matrices A such that AT = A).
(ii) Skew-symmetric matrices (i.e. matrices A such that AT = −A).
(iii) Orthogonal matrices (i.e. matrices A such that AT = A−1).
(iv) Singular matrices.
(v) Invertible matrices.
(vi) Echelon matrices.
(vii) Reduced echelon matrices.
----
I'd appreciate some guidance on how to tell which of the above apply.. is it the same as showing that vectors in a subset are subspaces when they're closed under addition and linear multiplication?
thanks.