Linear Algebra:

# 19 Given the linear transformation T( X, , X 2 ) = ( X,+ x 2 , X2 , 4X1 +X2 ) determin dim (kernel (T)) and the dim (range (T)).# 20 A function T from Rn to RMis given. Either prove that Tis a linear Transformation by showing that It satisfies the two requirements of a transformation, or show that it is not by using a Counterexample, with numbers T( X1, X21X3) = - 7XI+ 2x2 - X3+ 4