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:(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Some subspace questions

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