6) If A is a 3×3 invertible matrix, then the nullity of A is 0? Explain

7) Which of the following is not a subspace of R^3 space, where a, b, c belongs to R? Explain
a)All vectors of the form (a, 0, c)
b)All vectors of the form (a, b, 0)
c)All vectors of the form (a, 1, 1)
d)All vectors of the form (a, b, c)

8)The statement “A vector space must contain at least two vectors.” is true or false? why? explain

9)
If A is a 4×5 matrix then what is the largest possible value of rank(A)? explain
a)2
b)3
c)4
d)5