- #1

vsage

13. The set of solutions to the system of linear equations

a - 2b + c = 0

2a - 3b + c = 0

is a subspace of R^3. Find a basis for this subspace

The book claims one of the possible bases is (1, 1, 1) but I don't see how. I mean I realize a = b = c from the above just am not making the connection why there has to be THREE 1's. Originally I had (1, 1) but I really can't remember why. Is it because since a, b and c are equal, all the solutions to the above in (a, b, c) format are given by d(1, 1, 1) where d is a scalar?