find a basis and dimension for the subspace

V=<(1;2;1;-1),(3;1;0;5),(0;5;3;-8)>

I'm new.please write specifically.thank you

Answer 1

[Wayne King]

    V1 = [1;2;1;-1]; V2 = [3;1;0;5]; V3 = [0;5;3;-8];
    V = [V1 V2 V3];
    rank(X)

The rank of the matrix is 2 meaning the dimension of the space spanned by the columns of the set of three vectors is a two-dimensional subspace of R^3. To find the basic columns

    R = rref(V);

The output of rref() shows how to combine columns 1 and 2 to get column three. Specifically,

3*V1-1*V2

[nam]

thank you.how about V={(x1,x2,x3,x4)R4;x1+x2-x3=0 &2x1-x3-x4=0}