Solve (if possible) each of the following systems of three equations in three variables using the method of GaussJordan elimination. (a) 3x1 + 6x2 - 3x3 = 6 -2x1 - 4x2 - 3x3 = -1 3x1 + 6x2 - 2x3 = 10 (b) X1 + 2X2 + X3 = 7 x1 + 2x2 + 2x3 = 11 2x1 + 4x2 + 3x3 = 18 (c) X1 + 2X2 - X3 = 3 2x1 + 4x2 - 2x3 = 6 3x1 + 6x2 + 2x3 = -1 (d) x1 + 2x2 + 3x3 = 8 3x1 + 7x2 + 9x3 = 26 2x1 + 6x3 = 11 (e) x2 + 2x3 = 5 x1 + 2x2 + 5x3 = 13 X1 + 2X3 = 4 (f) X1 + 2x2 + 8x3 = 7 2x1 + 4x2 + 16x3 = 14 X2 + 3X3 = 4

PSCI2012 KEY: Red Words: Important Key terms Chapter 2 State Key Problem: state strong enough to protect us is also strong enough to tyrannize us I. Why do we have govt Pursuit of self – interst doesn’t work Need balance between individual and collective benefits Prisoner’s dilemma: only make sat least 1 player benefit o Need to find 3 party enforcer o For “collective good” o *individual decisions can lead to collectively good outcomes Hobbes’s Problem: state of nature in which humanity was locked in prisoner’s dilemma o Life under state of nature would suck o Solution! Leviathan