The linear transformation is given as $T: M_{3,3} \to M_{3,3}$ defined by $T(A) = 1/2(A+A^T)$. This is also known as the symmetrization operator.
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No idea how to approach. Please help! – youngdev Dec 08 '15 at 17:06
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Hint: The question is asking the following: which matrices $A$ satisfy $T(A) = 0$? The answer is that this only occurs for matrices that satisfy...?
Ben Grossmann
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Wouldn't it just be a 3x3 zero matrix? Also, why would it be asking which matracies A satisfy T(A) = 0 when T(A) is given as 1/2(A+A^T)? Confused :( – youngdev Dec 08 '15 at 17:11
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To your second question, that's exactly what the "kernel of a transformation" is – Ben Grossmann Dec 08 '15 at 17:15
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Quick follow up, would there then not be 3 matrices for each dimension a, b and c? – youngdev Dec 08 '15 at 17:23
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I don't know what your question means. Yes, the kernel should be a $3$ dimensional subspace of $M_{3 \times 3}$. – Ben Grossmann Dec 08 '15 at 17:30