Unformatted text preview: ”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€” CHAPTER 7. â€”â€” ,
resulting in , , . The corresponding solution is x The initial conditions x e , we solve the equations ,
resulting in , , . The corresponding solution is x The initial conditions x e , we solve the equations ,
resulting in , , . The corresponding solution is x
Therefore the fundamental matrix is 12. The solution of the initial value problem is given by ________________________________________________________________________
page 407 â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€”â€” CHAPTER 7. â€”â€”
x x 13. Let It follows that is a scalar matrix, which is invertible, since the solutions are linearly independent.
Let
. Then The th column of the product matrix is
x,
which is a solution vector, since it is a linear combination of solutions. Furthermore, the
columns are all linearly independent, since the vectors x are Hence the product is
a fundamental matrix. Finally, setting
,
I . This is precisely the
definition of
.
14....
View
Full Document
 Spring '08
 Staff
 Linear Algebra, eigenvector

Click to edit the document details