MAT223H1 Lecture Notes - Augmented Matrix, Gaussian Elimination
Document Summary
We will give two solutions to this problem. But then 2 = 4, which is nonsense. So the system has no solutions in this case. (b) notice that if we let c = d = 4 then the third equation becomes or equivalently, after dividing through by 4, 4x1 + 4x2 = 8 x1 + x2 = = 2, which is exactly the rst equation. So we may ignore the third equation in this case and consider the simpler system x1 + x2 = 2 ax1 + bx2 = 4. Now it"s easy to nd examples where this system has a unique solution. Keeping in mind that we want to nd non-zero values of a and b, let"s try a = 1 and b = 1. By solving the resulting simultaneous equations, we get the unique solution x1 = 1 and x2 = 3.
