kingyof2thejring
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Three vectors are linearly independent iff The vectors are not on the same plane. Three vectors are linearly dependent ⇔ The vectors are on the same plane. Is this true.
Linearly Independent Vectors: Same Plane?
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kingyof2thejring said:Three vectors are linearly independent iff The vectors are not on the same plane. Three vectors are linearly dependent ⇔ The vectors are on the same plane. Is this true.
Yes, it is true, if you are talking about vectors in V^3(O), i.e. radius vectors.
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That's what "if and only if" (iff) means! "Three vectors are linearly independent iff The vectors are not on the same plane" means two things:kingyof2thejring said:Three vectors are linearly independent iff The vectors are not on the same plane. Three vectors are linearly dependent ⇔ The vectors are on the same plane. Is this true.
If the vectors are not on the same plane then the vectors are linearly independent" and "Three vectors are linearly independent only if the vectors are not on the same" which is the same as "if three vectors are linearly independent, then they are not on the same plane", exactly the statement you are asking about.
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