Linear Algebra True and False Circle T if the given statemen

Linear Algebra: True and False

Circle T if the given statement is true and circle F if not so. There is a real 3 Times 3 matrix with no real eigenvalues. There is a real 3 Times 3 matrix with no complex eigenvalues. Every eigenvalue of a complex symmetric matrix is real. Every eigenvalue of a real symmetric matrix is real. If lambda is a complex eigenvalue with a corresponding complex eigenvector v, then lambda is a complex eigenvalue of A and v is a complex eigenvector of A corresponding to lambda. (u, v + w) = (v, u) + (w, u). (ku, kv) = k^2(u, v). If (u, v) = 0, then u = 0 or v = 0. If ||v||^2 = 0, then v = 0. If A is an n Times n matrix, then (u, v) = Au Av defines an inner product on R^n.

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