Determine whether the vector (9,0,9) is a linear combination of the vectors
(1,1,0), (1,0,1), (2,1,1) and (0,1, −1).
There is an obvious linear combination:
(9,0,9)=0⋅(1,1,0)+9⋅(1,0,1)+0⋅(2,1,1)+0⋅(0,1,−1).(9,0,9)=0\cdot(1,1,0)+9\cdot(1,0,1)+0\cdot(2,1,1)+0\cdot(0,1,-1).(9,0,9)=0⋅(1,1,0)+9⋅(1,0,1)+0⋅(2,1,1)+0⋅(0,1,−1).
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