Consider the system of linear equations x1 + 2x2 + x3 = 3
Consider the system of linear equations
x1 + 2x2 + x3 = 3
2x1 + 3x2 + x3 = 3
3x1 + 5x2 + 2x3 = 1
The system has
(a) infinite number of solutions
(b) exactly 3 solutions
(c) a unique solution
(d) no solution
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(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.
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