Linear algebra: proving these vectors form a basis of R4


  1. Given v1 = (1, 0, 1, 2)T
    , v2 = (0, 1, 1, 0)T
    , v3 = (−1, 2, 1, 0)T
    , v4 = (0, 0, 1, 0)T
    .
    (i) Prove that v1, v2, v3, v4 form a basis of R4
    ;
  2. Given v1 = (1, 0, 1, 2)T
    , v2 = (0, 1, 1, 0)T
    , v3 = (−1, 2, 1, 0)T
    , v4= (0, 0, 1, 0)T
    .
    (i) Prove that v1, v2, v3, v4 form a basis of R4
    ;

I have no idea because i thought basis are pivot columns like (1 0 0 0),(0 1 0 0), but the above are not pivot columns.
Thanks a lot