Question: A1. Dene the terms linear combination, linear dependence and linear independence as applied to vectors. Suppose ad: and c are three vectors in R .

A1. Dene the terms linear combination, linear dependence and linear independence

A1. Dene the terms linear combination, linear dependence and linear independence as applied to vectors. Suppose ad: and c are three vectors in R" . Show that: (i) if a,b and c are linearly dependent then there exist scalars {1,5 and 7, not all zero, such that ua+l3b+yc= , (ii) if there exist scalars {1J3 and 7, not all zero, such that ua+l3b+yc= then a,h and c are linearly dependent. State the generalisation of this result to the case of k vectors in R\" . Use the generalisation to prove the following statements: {a} Any set of vectors containing the zero vector is linearly dependent. (b) Any set of more than n vectors in R" is linearly dependent

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