Question

show that the following are spanning sets for R3.

{(1,1,1)transpose (1,1,0)transpose (1,0,0)transpose}

plz show full solution

Answer 1

Put into a matrix and use row-operations to get three linearly independent rows: (1,0,0), (0,1,0) and (0,0,1).

Answer 2

1 0 0
1 1 0
1 1 1

subtract row 1 from row two:
1 0 0
0 1 0
1 1 1

now subtract row 1 and row 2 from row 3:
1 0 0
0 1 0
0 0 1

we are in reduced row-echeon form, so the three rows must form a linearly independent set which spans \[\mathbb{R}^3\]