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T4 - ERG 2018 Tutorial 4 1 Vector space subspace Span and...

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ERG 2018 Tutorial 4 September 30, 2008 1. Vector space, subspace, Span and linear independence For the strict definition of vector space and subspace , you can refer to textbook P.189 and P.197. Let 12 ,,, k v vv K be vectors in a vector space V. A vector v in V is called a linear combination of k v K if 1 1 22 1 k k k jj j v a v a v a v av = =+ + += L Consider { } k S v = K as a set of vectors in V, then span S is the set of all vectors in V that can be written as linear combinations of k v K . The vectors k v K are said to be linearly independent if, whenever 1 1 0 kk a v a v + + L , then 0 k a aa ==== L . Otherwise, they are linearly dependent . Note that span k v K is a subspace of V (P.210) 1.1 Example: Linearly Independent (LI) Determine whether or not the set 123 {,,} vvv is linearly dependent, where 1 21 2 , 1 ,1 312 -   == =- -  2. The Basic Unit Vectors in 3-D Vector Space (V= 3 ¡ ) 100 0 , 1 ,0 001 ijk ===

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T4 - ERG 2018 Tutorial 4 1 Vector space subspace Span and...

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