Question: If f and g are in b(j), the vector space of all functions with continuous derivatives, then the determinant is called the Wronskian off and

If f and g are in b(j), the vector space of all functions with continuous derivatives, then the determinant

is called the Wronskian off and g [named after the Polish-French mathematician Josef Maria HoeneWronski (1 776- 1 853), who worked on the theory of determinants and the philosophy of mathematics]. Show that f and g are linearly independent if their Wronskian is not identically zero (that is, if there is some x such that W(x) ‰ 0).

w(x)=|f(x) g(x) f(x) g )

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