Math for economics

Dene the terms linear combination, linear dependence and linear independence as applied to vectors. Suppose a,band c arethree vectors in R\" . Show that: (i) if a,b and c are linearly dependent then there exist scalars o,|3 and fr, not all zero, such that a+|3b+tc=0 , (ii) if there exist scalars u,|3 and 1!, not all zero, such that oa+|3b+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