Suppose that one of the vector functions x1.t / D x11.t /

Chapter , Problem 42

(choose chapter or problem)

Suppose that one of the vector functions x1.t / D x11.t / x21.t / and x2.t / D x12.t / x22.t / is a constant multiple of the other on the open interval I . Show that their Wronskian W .t / D jxij .t /j must vanish identically on I . This proves part (a) of Theorem 2 in the case n D 2.

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