Question: Suppose V is a nonzero, finite-dimensional vector space over an arbitrary field F , and that T : V V is a linear operator. Prove

Suppose V is a nonzero, finite-dimensional vector space over an arbitrary

field F, and that T : V V is a linear operator. Prove that there exists an ordered

basis B for V such that the first column of the matrix [T]B is either(,0,...,0,0)

for some scalar F, or (0,1,0...,0).

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