(d) x1 + 2x2 + x3 = 3
2x1 + 3x2 + x3 = 3
3x1 + 5x2 + 2x3 = 1
A quick observation tells us that the sum of first two equations yields
(x1 + 2x2 + x3) + (2x1 + 3x2 + x3) = 3 + 3
⇒ 3x1 + 5x2 + 2x3 = 6
But this contradicts the third equation, i.e.,
3x1 + 5x2 + 2x3 = 1
As such the system is inconsistent and hence it has no solution.
