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Given the three eigenvalues A1 = 0, A2 = A3 = 2 of the real symmetric matrix A of order 3, and the eigenvector corresponding to the eigenvalue 0 is (1,0, - 1) ^ t, find the matrix A
Solution: let the eigenvectors of a belonging to eigenvalue 2 be (x1, X2, x3) '. Because the eigenvectors of real symmetric matrix A belonging to different eigenvalues are orthogonal, so x1-x3 = 0. Its basic solution system is: (1,0,1)', (0,1,0) ', and the orthogonality unites the three eigenvectors to P1 = (1 / √ 2,0, - 1 / √ 2)', P2 = (1 / √ 2,0,1 / √
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