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Mathematics-2014: Answer Writing Challenge – 5


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; (ii) the null space of T.



3) Describe explicitly a linear transformation from V3(R) into V3(R) which has its range spanned by

(1,0,-1) and (1,2,2).