Question

The following system of equations: x1 + x2 + x3 = 1, x1 + 2x2 + 3x3 = 2, x1 + 4x2 + αx3 = 4 has a unique solution. Possible value(s) for α is/are:

• A. 0
• B. Either 0 or 1
• C. One of 0, 1, or -1
• D. Any real number other than 5

Hint:

For unique solutions, ensure the determinant of the coefficient matrix is non-zero.

Answer 1

The Correct Option is D

To determine the unique solution, calculate the determinant of the coefficient matrix: det = α − 8. For a unique solution, the determinant must not be zero: α − 8 ≠ 0. Thus, α can be any real number except 8.