How can I extract the coefficients of all monomials in a multivariate polynomial?

For example if f=ax^2+bxy^3+2 then I want

coeff(f,x^2)=a

coeff(f,xy^3)=b

coeff(f,1/2)=4

coeff(f,1/10)=20 and...

I know the Wronskian command. I want to use this command for detecting linearly dependence or independence of some polynomials. I know that the polynomials  are  linearly independent if the Wronskian is not zero.  Conversely, if the Wronskian vanishes  then the polynomials are linearly dependent. Now I want to know that how can I find the coefficient vector if the polynomials are dependent by Wronskian command?

For example if [f1,f2,f3] be a list of polynomials s.t. a1f1+a2f2+a3f3=0. How can I find a1, a2, a3? 

How  we can decide whether a polynomial f is a linear combination of some polynomials g1,...,gm?

For example if f=x^2+y^2 and g1=y+x^2 , g2=y^2-y then f=g1+g2.

Let M be the matrix [[]] means that a matrix without any array. If we call RowDimension(M) then it output is 1 and we know that it is zero. What I have to do? It is hilarious that the RowDimension([[1]])=RowDimension([[]])!!!

I know that the "Rank(M)" command of Maple computes the rank of matrix M and I know that the "RowDimension(M)" gives the number of rows of M. Is there any command to gives the number of nonzero rows or columns of M?

For example, Let M be the following matrix. I want [2,3] as the output  where the first component ( second component. resp) is the number of nonzero rows (nonzero columns. resp) of M.

                              [1  5  6]

                       M=   [0  0  0]

                              [2  3  5]