# Then notice that n has nilpotency 2 then using 1 7

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Unformatted text preview: line solution is obtained, where is the eigenvector associated with . However the full phase portrait is most easily visualized using a computer. phase portrait drawn by a computer Example. Solve the initial value problem , where . Since is upper triangular, the eigenvalues can be read off the main diagonal. has multiplicity and has multiplicity . The generalized eigenspace associated with is . Find . A choice for generalized eigenvectors spanning generalized eigenspace associated with is is and . Find The . Let . The transformation matrix is . Notice that is block diagonal. Its inverse is also block diagonal, with each block the inverse of the corresponding block in Then . We are now ready to find and Then is given by and where . Obtain It’s easy to check . 8 Chapter 2 part B , where . The solution of the initial value problem is Jordan Form Let where or . cannot always be diagonalized by a similarity transformation, but it can always be transformed into Jordan canonical form, which giv...
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## This document was uploaded on 02/24/2014 for the course MATH 512 at Washington State University .

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