Question: Consider the matrix A = 5 7 -5 0 0 Find three eigenvectors of A that form a basis 0 1 for R. Then

Consider the matrix A = 5 7 -5 0 0 Find three eigenvectors of A that form a basis 0 1 for R. Then express the

Consider the matrix A = 5 7 -5 0 0 Find three eigenvectors of A that form a basis 0 1 for R. Then express the vector 1 with respect to this basis. (Hint: A square matrix whose transpose is equal to itself is called symmetric. It is known that eigenvectors of a symmetric matrix corresponding to different eigenvalues are orthogonal to each other.)

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