Answer:
Results are (1) True. (2) False. (3) False. (4) True. (5) True. (6) True.
Step-by-step explanation: 
Given A is an  matrix.  Let
 matrix.  Let  be the corresponding linear transformationover the field F and
  be the corresponding linear transformationover the field F and  be identity vector in V. Now if
 be identity vector in V. Now if  .
.
(1) The kernel of a linear transformation is a vector space : True.
Let  , then,
, then,

hence the kernel is closed under addition.
Let  , then
, then

 and thus Ket(T) is closed under multiplication
 and thus Ket(T) is closed under multiplication
Finally, fore all vectors  ,
, 


Thus Ker(T) is a subspace.
(2) If the equation Ax=b is consistent, then Col(A) is  : False
 : False
if the equation Ax=b is consistent, then Col(A) must be consistent for all b.
(3) The null space of an mxn matrix is in  
 
: False
The null space that is dimension of solution space of an m x n matrix is always in  .
.
(4) The column space of A is the range of the mapping  
 
: True.
(5) Col(A) is the set of all vectors that can be written as Ax for some x. : True.
Here Ax will give a linear combination of column of A as a weights of x. 
(6) The null space of A is the solution set of the equation Ax=0. 
: True