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  3. 1 1 point the matrix a 2 1 4 2 2 2 2 4 2...

1 1 point The matrix A 2 1 4 2 2 2 2 4 2...

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Algebra

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1 1 point The matrix A 2 1 4 2 2 2 2 4 2 1 1 2 2 0 The eigenvalue is and has multiplicity k For this eigenvalue the eigenvector v has components a and b that satisfy 2 2 a 1 b 0 1 a 4 2 b 0 which is the system such that a 8 Since there is no other linearly independent solution this eigenvalue is defective Following the algorithm for defective multiplicity 2 eigen values find a nonzero solution v2 of the equation A 2 v 0 Let V2 has characteristic equation det Choosing a 1 for the eigenvector is v b a b 0 a b 0 A 2 V V C a where c d are to be determined Then A 2 v2 v is the system c d c d Choosing c 1 V2 1 12 11 1 A general solution of the differential equation x t Ax is given by x t C x1 1 c x2 1 where x t vie x2 1 v te v e Answer s submitted incorrect 41

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