SOLUTION: the problem: Prove that (1,0,0,1) and (0,1,1,0) are linearly independent. I think they are dependent, am i missing something?

Question 165494: the problem:
Prove that (1,0,0,1) and (0,1,1,0) are linearly independent. I think they are dependent, am i missing something?
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
The previous discussion regarding dot product was not correct.
I mixed up orthogonality and linear independence.
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For these two vectors to be linearly independent, then a combination of these two vectors with two scalar multipliers can only be zero when the multipliers are zero.
(1,0,0,1)A+(0,1,1,0)B=(0,0,0,0) only if A=B=0.
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Look at each individual component of the vectors.
1.(1)A+(0)B=0
2.(0)A+(1)B=0
3.(0)A+(1)B=0
4.(1)A+(0)B=0
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From 1 and 4,
A=0
From 2 and 3,
B=0
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Therefore, you proved that they are linearly independent because the combination of the two vectors can only equal the zero vector when A=B=0.
Sorry for the confusion.

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