Question 165494
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.