If S is the set of distinct values of b for which the following system of linear equations x + y + z = 1 x + a y + z = 1 a x + b y + z = 0 has no solution, then S is:

Step-by-step solution

For no solution D = 1 1 1 1 a 1 a b 1 = 0 Expanding the determinant along the first row, we get D = - a - 1 2 = 0 ⇒       a = 1 For a = 1 , first two planes are coincident. Now, we have x + y + z = 1   &   a x + b y + z = 0 For no solution, these two planes are parallel. ⇒ 1 a = 1 b = 1 1 ⇒ a = 1   &   b = 1 . ∴       b = 1  ⇒  it is a singleton set