Consider the matrix 202 -1 21 T41 202 A = 0 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) 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. c) Determine if the matrix (A+AT) is positive definite, negative definite or indefinite. Hint: this can be determined without computing the eigenvalue decomposition (e.g. using properties of the eigenvalues and/or using Hermite's theorem).

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