3. Let
A = \begin{pmatrix} 2 & 4 & 3 \\ 9 & 6 & 3 \\ -1 & 3 & 4 \\ 1 & 1 & 1 \end{pmatrix}.
(a) (1 point) What is the rank of A? Explain how you derive your answer.
(b) (3 points) Is it possible to find a matrix B such that BA = I3, where I3 is the order
3 identity matrix? If so, find all possible B. If not, explain why.
(c) (2 points) Is it possible to find a matrix B such that AB = I4, where I4 is the order
4 identity matrix? If so, find all possible B. If not, explain why.
(d) (2 points) Is it possible to find a nonzero vector v \neq 0 such that Ax = v is con-
sistent, and v is in the nullspace of A$^T$? If it is, provide an example. Otherwise,
explain why not.
