Question: Question below Consider the matrix 2000 _Ule A0020 0&01 (a) Without doing any calculations, look at A nd one of its eigenvectors; explain. (In) Find

Question below

Consider the matrix 2000 _Ule A0020 0&01 (a) Without doing any calculations, look at A nd one of its eigenvectors; explain. (In) Find all value-5E k such that the eigenvalues for A are exactly A1 U and A2 2. Choose one such value of k, and diagonalize A. (For this partI show all of your work, but feel free to check your calculations using computational software.)I (c) Still using your chosen is, pick one eigenvector v1 for A with eigenvalue A1 = U and another eigenvector v2 for A with eigenvalue )'2 2, and ire-rib" that in -v2 U. (How did 1 know that this would happen without even knowing any of the choices you made?! Read on...) (a) Bonus: Now let B be an arbitrary matrix such that B : BT, and suppose that in, v; are eigenveetors of B corresponding to eigenvalues A1 = and A2 = 2. Prove that v1 and v2 are always orthogonal. (Don't think: about this probtem unless you have timeit's Spicy!)

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