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Examine the following vectors for linear...

Examine the following vectors for linear independence :
i. `veci+vecj+veck, 2veci+vecj-veck, -veci -2vecj+2veck`
ii. `3veci+vecj-veck, 2veci-vecj+7veck, 7veci-vecj+13veck`

Text Solution

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(i) Let `veca= veci+vecj+veck, vecb= 2veci+3vecj-veck, vecc= -veci-2vecj+2veck`
`" "|{:(1,,1,,1),(2,,3,,-1),(-1,,-2,,2):}|=-1`
Hence, vectors are non-coplanar and linearly independent.
(ii) Let `veca= 3veci+vecj-veck, vecb= 2veci-vecj+ 7veck, vecc= 7veci-vecj+13 veck`
`" "|{:(3,,1,,-1), (2,,-1,,7), (7,,-1,,13):}|=0`
Hence, vectors are coplanar and linearly dependent.
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