MapleDeterminants.mws

Computing a Determinant

Wronskian Example

This worksheet demonstrates computing the Wronskian for the functions f(x) = exp(2*x) , g(x) = exp(-3*x)  and h(x) = exp(4*x) .

>    with(LinearAlgebra):
M1 := Matrix(3,[[exp(2*x),exp(-3*x),exp(4*x)],[2*exp(2*x),-3*exp(-3*x),4*exp(4*x)],[4*exp(2*x),9*exp(-3*x),16*exp(4*x)]]);    

M1 := Matrix(%id = 18489144)

>    Determinant(M1);

-70*exp(2*x)*exp(-3*x)*exp(4*x)

You could use the fact that the determinant to be computed will equal exp(3*x)  times the determinant of the matrix M2 given below.

>    M2 := Matrix(3,[[1,1,1],[2,-3,4],[4,9,16]]);

M2 := Matrix(%id = 18501304)

>    Determinant(M2);

-70

I shouldn't show you this but Maple does have a Wronskian command.

>    with(linalg): 

Warning, the previous binding of the name GramSchmidt has been removed and it now has an assigned value




Warning, the protected names norm and trace have been redefined and unprotected

>    A := vector([exp(2*x),exp(-3*x),exp(4*x)]);

A := vector([exp(2*x), exp(-3*x), exp(4*x)])

>    W:=wronskian(A,x);

W := matrix([[exp(2*x), exp(-3*x), exp(4*x)], [2*exp(2*x), -3*exp(-3*x), 4*exp(4*x)], [4*exp(2*x), 9*exp(-3*x), 16*exp(4*x)]])

>    det(W);

-70*exp(2*x)*exp(-3*x)*exp(4*x)

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