Answer (c), and (d) only. Exercise 4.7 Consider, for varying a € R, the matrix: 01 a 1 0 2 2 2 a +1 Aa = a) Establish if the subspace ((1,0,0), (0, 1,0)) contains eigenvectors for Aa. b) Determine the eigenspaces of Aa. c) Say for which a € R the matrix is diagonalisable. d) For a 0, determine a matrix H such that H-¹AH is upper triangular.

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