My class hasnt learned row reduction linear independence ye

My class hasn\'t learned row reduction / linear independence yet. Help.

Describe geometrically (line, plane, three-dimensional space) the span of d) -1 and 1 and 0 -1

Solution

Denote the vectors by :x1,x2,x3

x1=(1,-1,0)

x2=(0,1,-1)

x3=(1,0,1)

(x1+x2+x3)/2=(1,0,0)

(x3-x1+x2)/2=(0,1,0)

x3-(x1+x2+x3)/2=(1,0,0)=(0,0,1)

Hence all the standard basis vectors lie in the span of these three vectors.

Hence the span of these three given vectors is the whole of 3 dimensional space because the standard basis vectors span the three dimensional space.