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page 355 —————————————————————————— CHAPTER 7. ——
of the other. However, there is no nonzero scalar, , such that
and
for all
. Therefore the vectors are linearly independent.
16. The eigenvalues and eigenvectors x satisfy the equation For a nonzero solution, we must have The eigenvalues are
x are solutions of the system , that is, and The two equations reduce to
, we have The components of the eigenvector . Hence x Now setting ,
with solution given by x
17. The eigenvalues and eigenvectors x satisfy the equation For a nonzero solution, we must have The eigenvalues are
becomes and , that is, For , the system of equations ,
which reduces to
Substituting . A solution vector is given by x
, we have
. The equations reduce to . Hence a solution vector is given by x 19. The eigensystem is obtained from analysis of the equation
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This note was uploaded on 03/11/2014 for the course MA 303 taught by Professor Staff during the Spring '08 term at Purdue UniversityWest Lafayette.
 Spring '08
 Staff

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