**Unformatted text preview: **1.13 ) is the trivial one. (a) Show that any collection of vectors which includes the zero vector is linearly dependent. (b) Show that a collection of two nonzero vectors { −→ v 1 , −→ v 2 } in R 3 is linearly independent precisely if (in standard position) they point along non-parallel lines. (c) Show that a collection of three position vectors in R 3 is linearly dependent precisely if at least one of them can be expressed as a linear combination of the other two. (d) Show that a collection of three position vectors in R 3 is linearly independent precisely if the corresponding points determine a plane in space that does not pass through the origin. (e) Show that any collection of four or more vectors in R 3 is linearly dependent . ( Hint: Use either part (a) of this problem or part (b) of Exercise 4 .)...

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