Consider the matrix A = 5 1 0 5 1 0 l-1 1 6 a) Diagonalize the matrix in the form A = SAS-¹, with S a matrix containing the (normalized) eigenvectors and A a diagonal matrix containing the eigenvalues. b) Is the matrix S an orthogonal matrix ? Why / why not? c) Using the eigenvalue decomposition computed in a), determine (including a short explanation!) a. the rank of the matrix A. b. the determinant of the matrix A. C. the null space of the matrix A.

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Q: Please solve without AI and clear handwriting. Thanks

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Q: Please solve without AI and clear handwriting.

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