linearly independent or linearly dependent.

how can i determine if vector v is a linear combination of the members of the S by using matlab ?

S = {(1,2,-1),(2,-1,0),(-1,8,-3)}

v = (0,5,-2)

Answer 1

[Matt J]

If [S,v] and S have the same rank, then the column vector v must be a linear combination of the columns of the matrix S.Testing this in your example,

S = [1,2,-1 ; 2,-1,0 ; -1,8,-3].' ;
v = [0,5,-2].';

isDependent = rank([S,v])==rank(S)

isDependent = logical
   1

[Jonas]

i like that solution, nice and clean!

Answer 2

[Jonas]

you could use something like

syms a b c; [sola,solb,solc]=solve(S{1}*a+S{2}*b+S{3}*c==v,a,b,c)