Zero Wronskian Does Not Imply Linear Dependence: We saw that a nonzero Wronskian implies linear independence but that the converse is not true. (see Example 12.) Another Example follows:
(a) Show that the Wronskian is zero for the functions

(b) Show that the function f and g are not linearly dependent but independent on (-(,().

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if 120, f(t) =12 and g(t)=t|11=