Mathematics-2014: Answer Writing Challenge – 5

ARCHIVES 18 September 2014 1) Show that the mapping T:V2(R)―›V3(R) defined as  T(a,b)=(a+b,a-b,b) is a linear transformation from V2(R) into V3(R).Find the range,rank,null space and nullity of T.     2) Let T:R3―›R3 be the linear transformation defined by : T(x,y,z)=(x+2y-z, y+z, x+y-2z). Find a basis and the dimension of (i) the range of T; …

Sociology-2014- Answer Writing Challenge – 15

ARCHIVES 18 September 2014 Answer in 250 words: 1) Examine Pareto’s analysis of the circulation of elites. It is valid for the modern  industrial societies? 2) Distinguish among power, prestige and authority. What are the different ways in  which an authority may gain legitimacy? Why does a changing society face crises of  legitimacy?