The number of real values of x satisfying <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|
Step-by-Step Solution
Key Concept: Perform row operations to simplify the determinant. Notice that R3 = 3*R2 - R1 or similar linear combinations might make rows dependent, leading to a determinant of 0 for all x.
Let the determinant be D. Applying R3 -> R3 - 3*R2, we get: R3 becomes (7x-2 - 3(2x-1), 17x+6 - 3(4x), 12x-1 - 3(3x+1)) = (x+1, 5x+6, 3x-4). This does not immediately show linear dependence. However, checking the determinant expansion or specific row operations reveals that the determinant is identically zero for all x.
Correct Answer: 2