Question

2. Let TE L(CT) be defined by T(zi, 22,23,24,25, 26, 27) = (4z1 + 22 + z3 + za, 432 + z3 + za, 423 + za, 424, 3Zg + Z6 + 27, 326 + 27, 327) Let B,(C7)-(q, e2: ea-e. es, eo, e } be the standard basis of C7 (25 pts.) Find M(T, B,(C) (25 pts.) Find the eigenvalues (kke. , For each eigenvalue, A (30 pts.) Find the eigenspace E(Ak,T) -(30 pts.) Find the generalized eigenspace G(Ak,T) . (30 pts.) What does the Jordan Form of M(T,B,(C) look like. . Identify the Jordan Basis. i. e. the basis with respect to which M(M(T93s(C7))93J) İs in Jordan Basis, Le the basi with respct to which MMT.() in Jordan Form: (30 pts.) Identify the Jordan Chains (30 pts.) Collect the Jordan Basis, Bj Although the computations are doable by hand, I strongly suggest using some technology to perform the basic matrix algebra

Answer 1

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