c It is given that a 3 3 matrix B has the following eigenvalues with corresponding eigenvectors w A1 95 w W1 19 2 14 12 95 W2 20

Question

c It is given that a 3 3 matrix B has the following eigenvalues with corresponding eigenvectors w A1 95 w W1 19 2 14 12 95 W2 20 Explain briefly how you know your answer is correct 5 14 A3 31 W3 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 x 3 matrix must have three different eigenvalues 59 13 14

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