5.8 Multiple solutions

The system

has an infinity of solutions. Isolating b in the second equation gives b=-2⋅c. Substitution into the first ^[1] gives a=0. For any value of c, there is a solution with (a=0, b+2⋅c=0)ℓ. In parametric form, the solution is (0, -2⋅c, c)ʋ which can be written as a function of c like this: fʋ(c)→(0, -2⋅c, c)ʋ, so for example, fʋ(0) has a solution (0, 0, 0). -->

Other solutions can be seen by evaluating fʋ(0) at several points. For example, (fʋ(i)|i∈1, 10, 3) evaluates to four solutions:

.