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Identify which of the following collections of matrices form a linear subspace in the linear space \(\operatorname{Mat}_{2 \times 2}(\mathbb{R})\) of all \(2 \times 2\) real matrices?

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Identify which of the following collections of matrices form a linear subspace in the linear space \(\operatorname{Mat}_{2 \times 2}(\mathbb{R})\) of all \(2 \times 2\) real matrices?

a) All invertible matrices.
b) All matrices that satisfy \(A^{2}=0\).
c) All anti-symmetric matrices, that is, \(A^{T}=-A\).
d) Let \(B\) be a fixed matrix and \(\mathcal{B}\) the set of matrices with the property that \(A^{T} B=\) \(B A^{T}\).
in Mathematics by Platinum (101k points) | 203 views

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