Ononot — Let V be the vector space of all 2 \times 2 matrices over \m

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Vectors & Spaceshard

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Let $V$ be the vector space of all $2 \times 2$ matrices over $\mathbb{R}$ . Let $W$ be the subspace of $V$ consisting of all symmetric matrices. Which of the following are true regarding the dimension and basis of $W$ ?