Unformatted text preview: tion.
2. Suppose that A is a matrix with an eigenvalue, , of multiplicity two
with associated eigenvector, v, and generalized eigenvector u. (That is,
3. Solve the following)IVPs. ). Recall that v and u are linearly independent
u satisﬁes (A
I u=v vectors. Let y1 (x) = e x v and y2 (x) = e x (u + xv). Use the deﬁnition
6
7
6
0
x
~,
x
x (0) =
toa) ~ =that y1 (x) and y2 (~ ) are linearly independent functions on IR.
show
1
2
0
3. In class we discussed the relationship between the Wronskian and linear 1
0
independence of 2 ~ ,
functions ~ (0) =are0solutions of a particular system of
which
b) ~ =
x
x
x
2
1
4
di erential equ...
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 Winter '14
 Linear Algebra, two second, linearly independent eigenvector, appropriately deﬁned vector

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