We can set up a matrix and use Gaussian elimination to figure out the dimension of the space they span.
⎝⎛100210321⎠⎞ R1=R1−2R2
⎝⎛100010−121⎠⎞
R1=R1+R3
⎝⎛100010021⎠⎞
R2=R2−2R3
⎝⎛100010001⎠⎞Since the rank of the matrix is 3, then the set {(1,2,3),(0,1,2),(0,0,1) of vectors generates or span R3.
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