3. Are these matrices diagonalisable? Justify your answers without much calculations 1 1 1 1 A...

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3. Are these matrices diagonalisable? Justify your answers without much calculations 1 1 1 1 A = 021 B = 021 003 001 111 1-21 C -22 1 D -2 21 001 1 1 3 Give an example of a matrix which is diagonalisable but not orthogo- nally diagonalisable. 4. Diagonalise the matrix 1 1 0 A 10 1 (5 marks) 0 1 1 Explain why all eigenvalues are real. Can this matrix be orthogonally diagonalised and why? If so find this orthogonal diagonalisation. Find A10 3. Are these matrices diagonalisable? Justify your answers without much calculations 1 1 1 1 A = 021 B = 021 003 001 111 1-21 C -22 1 D -2 21 001 1 1 3 Give an example of a matrix which is diagonalisable but not orthogo- nally diagonalisable. 4. Diagonalise the matrix 1 1 0 A 10 1 (5 marks) 0 1 1 Explain why all eigenvalues are real. Can this matrix be orthogonally diagonalised and why? If so find this orthogonal diagonalisation. Find A10