1. In the following sets of equations,

(a) and

(b) have unique (basic) solutions,

(c) has an infinity of solutions, and

(d) has no solution. Show how these results can be verified using graphical vector representation. From this exercise, state the general conditions for vector dependence-independence that lead to unique solution, infinity of solutions, and no solution.

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(a) x + 3x2 = 2 3x1 + x2 = 3 (c) 2x+6x2 = 4 (b) 2x + 3x2 =1 2x - x2 = 2 (d) 2x, 2x - 4x2 = 2 x + 3x2 = 2 -x+2x2 = 1