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Problem 63: Determine whether it is a subspace of the given vector space $\V$
$V = M_n(\R)$, and S is the subset of all n×n invertible matrices

Problem 63: Determine whether it is a subspace of the given vector space $\V$
$V = M_n(\R)$, and S is the subset of all n×n invertible matrices.

Solution:
$S= \{A \in M_n(\R) : A$ is invertible$\}$ is not a subspace of $M_n(\R)$ because $0_n \notin S$.

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