Consider the system of equations : x + ay = 0, y + az = 0 and z + ax = 0. Then the set of all real values of 'a' for which the system has a unique solution is :
Step-by-Step Solution
Key Concept: A homogeneous system of linear equations has a unique solution (the trivial solution x=y=z=0) if and only if the determinant of the coefficient matrix is non-zero.
The system is: x + ay + 0z = 0, 0x + y + az = 0, ax + 0y + z = 0. The coefficient matrix is A = [[1, a, 0], [0, 1, a], [a, 0, 1]]. The determinant |A| = 1(1 - 0) - a(0 - a^2) + 0 = 1 + a^3. For a unique solution, |A| != 0, so 1 + a^3 != 0, which means a^3 != -1, so a != -1. Thus, the set of all real values of 'a' is R - {-1}.
Correct Answer: B