(a) Prove that if s is an eigenvector of a nonsingular matrix A then it is...

   

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(a) Prove that if s is an eigenvector of a nonsingular matrix A then it is also an eigenvector of A-. (b) Show that every square matrix A and its transpose AT have the same eigen- values. (c) Prove that no nonzero eigenvector can belong to two different eigenvalues. (a) Let Find A100 (b) Let 201 A=0 20 102 [100 1 0 11 1 B 0020 0002 Find the eigenvalues and eigenvectors of B. (a) Prove that if s is an eigenvector of a nonsingular matrix A then it is also an eigenvector of A-. (b) Show that every square matrix A and its transpose AT have the same eigen- values. (c) Prove that no nonzero eigenvector can belong to two different eigenvalues. (a) Let Find A100 (b) Let 201 A=0 20 102 [100 1 0 11 1 B 0020 0002 Find the eigenvalues and eigenvectors of B.