Ononot — Let V be the vector space of 3 \times 3 matrices. Consider t

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Vectors & Spaceshard

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Let $V$ be the vector space of $3 \times 3$ matrices. Consider the subspace $W = \{ A \in V \mid \text{tr}(A) = 0 \}$ . What is the dimension of the subspace $S \cap W$ , where $S$ is the space of symmetric $3 \times 3$ matrices?