Unformatted text preview: z , z = re iθ , obtain: z 3 , √ z , 1 /z 2 , and ¯ z 4. Obtain all values of 4 √2 i , i.e. all complex numbers z such that z 4 =2 i . 5. Consider the following system of ordinary diﬀerential equations (ODEs): d x dt = A x , A = ± 21 3 ! . (2) (a) Obtain the eigenvalues and the eigenvectors of the matrix A . (b) Obtain the general solution of this equation. (c) Obtain the solution that corresponds to the initial conditions x (0) = (1 ,1), 6. Solve problem 5 for the following system of ODEs: d x dt = A x , A = ± 12 2 1 ! . (3)...
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 Spring '08
 Hawkins
 Linear Algebra, Vector Space, Complex number

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