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(c) It is given that a 3 3 matrix B has the following eigenvalues with corresponding eigenvectors Wk 19 20 1 = 95, w

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(c) It is given that a 3 3 matrix B has the following eigenvalues with corresponding eigenvectors Wk 19 20 1 = 95, w W1 = -2 14 2 = 95, w2 ; = -5 A3 = 31, w3 -14 = 59 -13 -14 Select the correct statement from the following list, then use the essay box to explain briefly how you know your answer is correct. B is diagonalisable, because B has three linearly independent eigenvectors B is diagonalisable, because B has infinitely many eigenvectors B is diagonalisable, because B has three real eigenvalues B is not diagonalisable, because B does not have three linearly independent eigenvectors B is not diagonalisable, because the eigenvalues of B are linearly dependent B is not diagonalisable, because B does not have three different eigenvalues it is impossible to tell from the given information whether B is diagonalisable or not the situation described is impossible because a 3 3 matrix must have three different eigenvalues Explain briefly how you know your answer is correct.

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