Consider the following system of equations in three real variables x1, x2 and x3: 2x1 - x2 + 3x3 = 1; 3x1 - 2x2 + 5x3 = 2; -x1 - 4x2 + x3 = 3. The system of equations has :
- A. No solutions
- B. A unique solution
- C. More than one but a finite number of solutions
- D. An infinite number of solutions
Answer: B. A unique solution
Explanation: Coefficient matrix determinant det = 2(−2·1 − 5·(−4)) − (−1)(3·1 − 5·(−1)) + 3(3·(−4) − (−2)(−1)) = 2(18) + 1(8) + 3(−14) = 36 + 8 − 42 = 2 ≠ 0. Since det ≠ 0, the linear system has a unique solution.