Unformatted text preview: ations. The relationship for arbitrary functions is more subtle. To see how, consider the following example
1
3
1
0
c) ~ =
x
~,
x
~ (0) =
x
2x
3
7
0
, if x 0
2 cos(x)
y 1 ( x) =
x
Note: it’s not hard to check your answers withx < 0 problems.
, if these
cos(x)
y 2 ( x) = 3x
3 cos(x) ,x IR (a) Use the deﬁnition to show that y1 (x), y2 (x) are linearly dependent
on x 0.
(b) Use the deﬁnition show that y1 (x), y2 (x) are linearly dependent on
x < 0.
(c) Use the deﬁnition show that y1 (x), y2 (x) are linearly...
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 Winter '14
 Linear Algebra, two second, linearly independent eigenvector, appropriately deﬁned vector

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