Wronskian vs. Determinant in Determining Linear Independence?

[kq6up]

It seems to me that if a row is able to be zeroed out through Gaussian reduction that the determinate of that matrix would equal zero. Therefore, we know that at least one of equations/vectors that constructed the matrix was formed from the other two rows. That is -- that equation is dependent on the other two basis vectors.

Why do we need the Wronskian to determine this?

Thanks,
Chris Maness

 

[SteamKing]

The Wronskian is a special type of determinant used to determine if a set of solutions to a differential equation is linearly independent:

http://en.wikipedia.org/wiki/Wronskian

See the section on "The Wronskian and linear independence".

 

[kq6up]

Ok, is it that Wronskians are for function space where all the basis are formed by functions of x, where the determinants are for -- say -- {x,y,z} vectors in cartesian space?

Chris