Discussion
Consider the following system of linear equations:
2x - y + z = 1
3x - 3y + 4z = 6
x - 2y + 3z = 4
This system of linear equations has
Answer: A
The system has no solution.
Subtract the first equation from the second:
\[ \begin{aligned} (3x - 3y + 4z) - (2x - y + z) &= 6 - 1 \\ x - 2y + 3z &= 5 \end{aligned} \]
But the third equation says \(x - 2y + 3z = 4\). The same expression cannot equal both 5 and 4, so the equations are inconsistent. In matrix terms, the coefficient matrix has rank 2 while the augmented matrix has rank 3.
A consistent system with a rank-deficient matrix would have infinitely many solutions, not exactly two or three, and a unique solution would need the coefficient matrix to be non-singular, which it is not here.
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