Let a ε complex numbers and distinct from 0.
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Let a be an element of complex numbers and distinct from 0. Prove that the eigenvectors of the transformation T : Complex numbers^2 -> complex numbers^2 given by T ( z , w ) = ( z + aw , w) span on 1-dimensional subspace of complex numbers^2 and give a basis for this subspace.
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Solution Summary
This solution is comprised of a detailed explanation to prove that the eigenvectors of the transformation T : Complex numbers^2 -> complex numbers^2 given by T ( z , w ) = ( z + aw , w) span on 1-dimensional subspace of complex numbers^2 and give a basis for this subspace.
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Since T(z,w) = (z + aw, w), then the matrix representation of T is (still denoted as T)
1 a
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