Use vectors to determine graphically the type of solution for each of the sets of equations below: unique solution, an infinite number of solutions, or no solution. For the cases of unique solutions, indicate from the vector representation (and without solving the equations algebraically) whether the values of x1 and x2 are positive, zero, or negative.

(a) a 5 4 1 -3 b a x1 x2 b = a 2

2 b

(b) a 2 -2 1 3 b a x1 x2 b = a 1

3 b

(c) a 2 4 1 3 b a x1 x2 b = a -4

-2 b

(d) a 2 4 1 2 b a x1 x2 b = a 6

3 b

(e) a -2 4 1 -2 b a x1 x2 b = a 4

2 b

(f) a 1 -2 0 0 b a x1 x2 b = a 1

1 b