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Identify which of the following collections of matrices form a linear subspace in the linear space \(\operatorname{Mat}_{3 \times 3}(\mathbb{R})\) of all \(3 \times 3\) real matrices?

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Identify which of the following collections of matrices form a linear subspace in the linear space \(\operatorname{Mat}_{3 \times 3}(\mathbb{R})\) of all \(3 \times 3\) real matrices?

a) All matrices of rank 1 .
b) All matrices satisfying \(2 A-A^{T}=0\).
c) All matrices that satisfy \(A\left(\begin{array}{l}1 \\ 0 \\ 0\end{array}\right)=\left(\begin{array}{l}0 \\ 0 \\ 0\end{array}\right)\).
in Mathematics by Platinum (101k points) | 173 views

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