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1. Let A be the 2x2 matrix in M_{2x2}(C), whose first row is (0,1) and second...

1. Let A be the 2x2 matrix in M_{2x2}(C), whose first row is (0,1) and second row is (-1,0).

(a) Show that A is normal.

(b) Find (complex) eigenvalues of A.

(c) Find an orthogonal basis for C^2, which consists of eigenvectors of A.

(d) Find an orthonormal basis for C^2, which consists of eigenvectors of A.

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