Are the following statements true or false? If true, prove the statement. If false, give a counterexample. 1. Assume X, Y E Rnxn satisfying XY = YX and x is a generalized eigenvector of X. Then, Yx is also a generalized eigenvector of X. 2. Let A E Rmxn. Then, rank(AA? ) = rank(A). 3. Let A E R4x6, and its null space is 3-dimensional. Then, for any b E R4, the equation Ax = b has a solution