Question: 0 0 3 The matrix B = 0 0 4 has characteristic equation >(25 - 12) = 0. 3 4 3 3 The eigenvectors of

0 0 3 The matrix B = 0 0 4 has characteristic equation >(25 - 12) = 0. 3 4 3 3 The eigenvectors of B for the eigenvalues 5 and -5 are 4 and -4 respectively. 5 (i) Find another linearly independent eigenvector of B. (4 marks) (ii) Find an orthonormal basis of R3 that consists of eigenvectors of B. (4 marks) (iii) Does there exist an orthogonal diagonalisation VTBV = D? If one exists, give the matrices V and D. If not, explain why not

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