Unformatted text preview: nvector u. deﬁnition
vectors. Let y1 x) = e x v and y2 ( ) = e x (u + xv). Use the (That is,
u satisﬁes (A y1 (x) u = v).(x) are2linearly and u are linearly independent
I ) and y2 dD = D 5p + 10
Recall that v independent functions on IR.
to show that
vectors. Let y1 (x) = e v and y2 (x) = e x (u + xv). Use the deﬁnition
3. In show we discussed the and) p is linearly independent of increase ofIR.
where D is the x) and relationship price. The Wronskian and linear
to class that y1 (demandy2 (x are the between therate functions on the
independence to the rate ofwhich are of the quantity.
price is equal of functions decrease solutions of a particular system of
3. In class we discussed the relationship between the Wronskian and linear
di erential equations. The relationship for arbitrary functions is more
(a) Write see how, consider the are solutions of for
4 .independence of afunctionsof di erential equations a particular system of
subtle. Todown system which following example D(t) and p(t) tha...
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- Fall '11
- Linear Algebra, Boundary value problem, Eigenvalue, eigenvector and eigenspace, Generalized eigenvector, di erential equations, andxgeneralized eigenvector u. deﬁnition