Wronskian and Linear Independence

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$Old$ November 5th, 2009, 01:51 AM

charikaar $charikaar is offline$

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$Default$ Wronskian and Linear Independence

(1) be the n-th order homogeneous differential equation which is represented in matrix form

(2)

If

are the solutions to (1), what are the correspondence solutions of (2)?

are the solutions to (1), then the corresponding solutions to 2 are the vectors

for all i.

Is this the correct matrix for solutions

Prove that the following two conditions are equivalent: Please help me get started.

(i)

are linearly independent;
(ii)

not equal to zero for some

in the interval I.

Thank you.

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