Linear independence of a set of vectors
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Linear independence of a set of vectors

[From: ] [author: ] [Date: 13-01-21] [Hit: ]
1) -(1/2)*(0,2)+(-1,1)=(0,0) when the right answer is (-1,1) -(3/2)*(0,2)+(-1,......
The vectors (1,2) ,(0,2) and (-1,1) are linearly dependent but how do you find the relation between them?
I tried finding it and I ended up with (-1,1) -(1/2)*(0,2)+(-1,1)=(0,0) when the right answer is (-1,1) -(3/2)*(0,2)+(-1,1)=(0,0). Why is it (3/2)?
Help please?

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Your answer gives (-1,1) - (0,1) +(-1,1) = (-2,1) and not (0,0).
For linear dependence you need a*(1,2)+b*(0,2)+c*(-1,1)=(0,0)
giving a-c=0 and 2a+2b+c=0 . Note that if you sub a=1, then c=1 and b=-3/2.
You can also have multiples of these.
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keywords: set,vectors,Linear,independence,of,Linear independence of a set of vectors
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