374 5.1 Note: When m1, m2, m3, and m4 are distinct real numbers, {m1*x,m2*x,m3*x,m4*x} is linearly independent.
374 5.1 Note: When m1, m2, m3, and m4 are distinct real numbers, is linearly independent.
{,,,}
m1*x
m2*x
m3*x
m4*x
F={,,,}
m1*x
m2*x
m3*x
m4*x
{,,,}
m1x
m2x
m3x
m4x
Wronski[F_]:=Table[D[F,{x,i-1}],{i,4}]
MatrixForm[Wronski[F]]
m1x | m2x | m3x | m4x |
m1x | m2x | m3x | m4x |
m1x 2 m1 | m2x 2 m2 | m3x 2 m3 | m4x 2 m4 |
m1x 3 m1 | m2x 3 m2 | m3x 3 m3 | m4x 3 m4 |
Simplify[Det[Wronski[F]]]
(m1+m2+m3+m4)x
This expression is never zero since the only way it could be zero is if =for some i not equal to j.
m
i
m
j
Note that in Mathematica, there is a built-in command called Wronskian!!
Wronskian[F,x]
(m1+m2+m3+m4)x