Let T:R 3 R be linear. Show that exist scalars a, b, and c such that
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Let T:R 3 → R be linear. Show that exist scalars a, b, and c such that T(x, y, z) = ax + by + cz for all (x, y, z) ∈ R 3 . Can you generalize this result for T: F n → F? State and prove an analogous result for T: F n → F m .
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