What is the dimension of the subspace of all 3x3 symmetric matrices?
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6
The dimension of the space of n x n symmetric matrices is given by n(n+1)/2. For n=3, this is (3*4)/2 = 6, corresponding to the 3 diagonal and 3 unique off-diagonal elements.
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- How many dimensions are in the subspace consisting of all symmetric 3x3 matrices?