The following system of equations: $$ x_1 + x_2 + x_3 = 1, \quad x_1 + 2x_2 + 3x_3 = 2, \quad x_1 + 4x_2 + \alpha x_3 = 4 $$ has a unique solution. Possible value(s) for $\alpha$ is/are:
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For unique solutions, ensure the determinant of the coefficient matrix is non-zero.
A unique solution is obtained when the determinant of the coefficient matrix, `α − 8`, is non-zero. This implies that `α` can be any real number except `8`.