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The first three vectors in the following statement are linearly independent. I put this statement into Wolfram Alpha and it tells the 4 vector set is linearly independent

linear independence of {(1,2,0,2), (1,1,1,0), (2,0,1,3),(1,1,1,1)}

However when I used them as columns of a matrix and row reduced it I found they were linearly dependent.

I then used a completely random number for the 4th vector -

linear independence of {(1,2,0,2), (1,1,1,0), (2,0,1,3),(1,20,156,133)}

and it tells me this is linearly independent too. So is Wolfram Alpha wrong?

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    @Jim_CS Yes, orthogonality is a stronger condition than linear independence. (orthogonal implies linear independence but converse is false)2012-04-20

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