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Suppose chat A is a 4 times 4 matrix with distinct eigenvalues 2, 5, .pdf

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Suppose chat A is a 4 times 4 matrix with distinct eigenvalues 2, 5, and 7. Let E, represent eigenspace associated with the eigenvalue lambda = 5. If dim (E, ) = 2, can we conclude that A is diagonalizable? Explain. Solution Yes. Distinct eigenvalues have linearly indepdnent eigenvectors So eigenvectors of :2,5,7 are linearly independent There is one eigenvector corresponding to 2 , one to 7 Since E_5 has dimension 2 so there are 2 linearly independent eigenvectors corresponding to 5 so making a total of 4 linearly independent eigenvectors A is of size 4x4 For an nxn matrix to be diagonalizable it must have n linearly independent eigenvectors HEnce, A is diagonalizable..

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Suppose chat A is a 4 times 4 matrix with distinct eigenvalues 2, 5, and 7. Let E, represent eigenspace associated with the eigenvalue lambda = 5. If dim (E, ) = 2, can we conclude that A is diagonalizable? Explain. Solution Yes. Distinct eigenvalues have linearly indepdnent eigenvectors So eigenvectors of :2,5,7 are linearly independent There is one eigenvector corresponding to 2 , one to 7 Since E_5 has dimension 2 so there are 2 linearly independent eigenvectors corresponding to 5 so making a total of 4 linearly independent eigenvectors A is of size 4x4 For an nxn matrix to be diagonalizable it must have n linearly independent eigenvectors HEnce, A is diagonalizable.

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Suppose chat A is a 4 times 4 matrix with distinct eigenvalues 2, 5, .pdf

  • 1. Suppose chat A is a 4 times 4 matrix with distinct eigenvalues 2, 5, and 7. Let E, represent eigenspace associated with the eigenvalue lambda = 5. If dim (E, ) = 2, can we conclude that A is diagonalizable? Explain. Solution Yes. Distinct eigenvalues have linearly indepdnent eigenvectors So eigenvectors of :2,5,7 are linearly independent There is one eigenvector corresponding to 2 , one to 7 Since E_5 has dimension 2 so there are 2 linearly independent eigenvectors corresponding to 5 so making a total of 4 linearly independent eigenvectors A is of size 4x4 For an nxn matrix to be diagonalizable it must have n linearly independent eigenvectors HEnce, A is diagonalizable.