A set of vectors {V1, V2,..., Vn} in a vector space V is called linearly dependent...

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A set of vectors {V1, V2,..., Vn} in a vector space V is called linearly dependent if we can find scalars 1,2,,rn, not all zero, such that r1v1 +r2v2 + + rnvn = 0 where the right hand side is the zero vector. To demonstrate that a given set of vectors is linearly dependent, it is a good idea to use the definition and row-reduction to explicitly find scalars that demonstrate the linear relation. If our investigation leads us to conclude that the only way to arrange a linear relation with right hand side being 0 is to use r1 r2 = rn = 0, then the set cannot be linearly dependent (i.e. the set is a linearly independent set). Let's show that {--0)--)--(C)} = , W = 4 u= For example 4 ru sv + tw = 0. -5 is actually a linearly dependent set by finding scalars r, s and t (not all zero) such that -26 & P. -4 [r, s, t] = Using this we can express one of the vectors as a linear combination of the others, for example A set of vectors {V1, V2,..., Vn} in a vector space V is called linearly dependent if we can find scalars 1,2,,rn, not all zero, such that r1v1 +r2v2 + + rnvn = 0 where the right hand side is the zero vector. To demonstrate that a given set of vectors is linearly dependent, it is a good idea to use the definition and row-reduction to explicitly find scalars that demonstrate the linear relation. If our investigation leads us to conclude that the only way to arrange a linear relation with right hand side being 0 is to use r1 r2 = rn = 0, then the set cannot be linearly dependent (i.e. the set is a linearly independent set). Let's show that {--0)--)--(C)} = , W = 4 u= For example 4 ru sv + tw = 0. -5 is actually a linearly dependent set by finding scalars r, s and t (not all zero) such that -26 & P. -4 [r, s, t] = Using this we can express one of the vectors as a linear combination of the others, for example

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Given i 6 Ab 11 As 0 t 26 1 4 Augmented matrix 11 11 6 4 1 0 O 1 O 4 Op... View the full answer