Answer
a. True
b. True
c. False
d. True
e. True
f. True
Work Step by Step
a. A nullspace is a subspace and every subspace is a vectorspace.
b. Theorem 3 (Page no 203)
c. Col A = {b : b = Ax for some x in $R^n$}
d. The kernel of a matrix transformation T(x) = Ax is the nullspace of A.
e. The range of a linear transformation T, from a vector space V to a vectorspace W, is a subspace of W. Every subspace is a vectorspace. Hence, It is true.
f. True (page no 206 last line)
