SOLUTION: Determine if the following sets of vectors are a basis for R3 : a) v1 = (1, 1, 0), v2 = (-1, 0, 0)

Question 929971: Determine if the following sets of vectors are a basis for R3
:
a) v1 = (1, 1, 0), v2 = (-1, 0, 0)
Found 2 solutions by Fombitz, TimothyLamb:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
No, you cannot form vectors that have a z component.
Example: a(1,1,0)+b(-1,0,0)=(0,0,1) has no solution.

Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
the vector k = (0,0,1) is clearly a member of R3
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but there's no linear combination of v1 and v2 that can represent the vector k
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therefore, v1 and v2 are NOT basis vectors for R3
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