1) Anta at A = (2 4) (3 6) a) Find determinant A. Is A invertible? b) Assume that x = (x) and b = [b1] (y) [b2] Write A * x = b as a system of linear equations. c) Show that if b = (3) (9/2), then A * x = b has infinitely many solutions. Draw the two corresponding straight lines and explain why the system has infinitely many solutions. d) Find a column vector b = (b1) (b2), so that A * x = b has no solutions.

2) Anta at A = [a 8] x = [x]. b = [b1] [2 4], [y], and [b2]

a) Show that when a 4 then Ax = b has exactly one solution. b) Anta at a = 4. Find conditions on b1 and b2 so that Ax = b has (i) infinitely many solutions and (ii) no solutions. c) Explain the results in (a) and (b) graphically.