Question: 3 2 Task 1. (20%) Let A = 2 be a symmetric real matrix. (a) Find eigenvalues and corresponding eigenvectors of A; (b) Determine

3 2 Task 1. (20%) Let A = 2 be a symmetric

3 2 Task 1. (20%) Let A = 2 be a symmetric real matrix. (a) Find eigenvalues and corresponding eigenvectors of A; (b) Determine whether the eigenvectors are orthogonal to each other, or not. If not, or- thogonalize them to each other; (c) Normalize the orthogonal eigenvectors; (d) Obtain the orthonormal matrix S that diagonalizes A; (e) Calculate S"AS for given symmetric real matrix A.

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