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linearly dependent and independent


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A set of vectors u1, u2,…, ur is linearly independent if x1u1+x2u2+…+xrur=0 holds only if x1=0, x2=0,…, xr=0. Otherwise, the set is linearly dependent. In 3-dimensional space, any set of four or more vectors must be linearly dependent. A set of three vectors is linearly independent if and only if the three are not coplanar. A set of two vectors is linearly independent if and only if the two are not parallel or, in other words, if and only if neither is a scalar multiple of the other.

Subjects: Mathematics.


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