3. (7 points) Decide whether the following statements are trueor false (give a short justication if you
want full points!):
(a) A homogeneous system of three equations and four variables hasa nontrivial solution.
(b) If u1; u2 are both solutions to the system Ax = b then(u1+u2)/2 is also a solution.
(c) You can find three vectors in R4, u; v;w, with u orthogonal tov, v orthogonal to w, but u is
not orthogonal to w.
(d) If A;B;C are nxn non-singular matrices, then (ABC)^-1 =C^-1A^-1B^-1
(e) There can be a 4x4 non-singular matrix A such that Ax = 0 has anon-trivial solution (i.e.
x is a solution with some non-zero entries).
(f) Every square matrix with 1's down the diagonal isinvertible
(g) If A is invertible, then A^2 is invertible too.
