Hi I got stuck with this homework question so I'm here to ask you guy for some advice

if x is a real number, the absolute value of x is

absulute value (x)=x, if x is equal or more than 0

=-x, if x is less than or equal to 0

let S={(x,/x/,2/x/)/x is a real number}U{0,2,4),(-1,3,6)} and let V = span(S)

Show that V is a plane which contains the origin. Find a subset of S that is a basis of V.

So I know that V = span(s) thereby it is a zero vector, thus it will contains the origin but how would I write some mathematics equation to show that?

so V=(0,0,0)+s(0,2,4)+t(-1,3,6) since it passed though the origin, how would I find the basis for a subset of V? since V is a subset of S

[0 0 -1]

[0 2 3]

[0 4 6] <--- the matrix for V, row 2 and 3 are linearly dependent to each other (did I made the matrices right?) is it possible for me to get a basis out of that matrices?

p,s I'm an international student so my English isn't great. to me, subspace, span and basis are very confusing so please dont yell at me