Answer to Question #340396 in Linear Algebra for Mpho

Question

Consider the vector space V = C²with scalar multiplication over the real numbers R, and let T : V → V be the linear operator defined by T (z1, z2) = (z1 − iz2, z2 − z2) . Let W be the cyclic subspace of V generated by w = (1 + 2i, 1 + i).

5.1 Find the T–cyclic basis β for W generated by w.

5.2 Find the characteristic polynomial of TW .

5.3 Find [TW ]β. 5.4 Explain whether T = TW

Answer 1

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