book Maths Puzzle Numerical Ability

given : V vect.space , T operator , rank(T2)=rank(T).
prove range of T and N(T) DISJOINT ( ZERO COMMON VECTOR ONLY)?

ALSO PLEASE: GIVEN :V,T ,T2 = 0 ,What will be R(T)& N(T) re

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book Other Question
Evaluate x to 5 significant digits

x = ln (4.3931 x 10^-11) Write the product below in simplest form without parentheses:

(y + 4) (y - 2)