The group A4 (even permutations of f1; 2; 3; 4g) with the operation has 12 elements. Is it isomorphic to .Z12; /? Is .A3; / .Z3; /?

Section 1.7 "Special Systems" of Equations SOME THEOREMS I. Given a system of linear equations, exactly one of the following possibilities holds: (A) The system has infinitely many solutions. (B) The system has no solution. (C)The system has exactly one solution. What happens if we have more unknowns than equations Let’s look at a couple of examples. 10 2 4 − 01 2 1 − x1 324 x =− 42 x Here, so 1 3 x2 321 x2 312 x 3 3 x There are infinitely many solutions. Second example: 120 − 000 1 From the second line, we see this has no solution. If we have 3 unknowns and 2 equations, is there a way to get a unique solution An Example with a