Day04HWsoln - Exercise Set 3 Solutions In this homework set we will practice nding eigenvalues and eigenvectors when the eigenvalues are either complex

Day04HWsoln - Exercise Set 3 Solutions In this homework set...

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Exercise Set 3 Solutions In this homework set, we will practice finding eigenvalues and eigenvectors when the eigenvalues are either complex or the matrix is defective. 1. Given a 2×2 defective matrixAwith double eigenvalueλ, eigenvectorvand generalized eigenvectorw, show that the function:eλt(tv+w)solves the differential equationx0=Ax. 2. Exercises 1, 3, pg. 409 (Section 7.6, solve with complex evals/evecs) Solutions in the text. 3. Exercises 1, 3, 7, pg. 429 (Section 7.8, solve with degenerate matrix) Solutions in the text.