If S is the set of distinct values of 'b' for which the following system of linear equations
x + y + z = 1
x + ay + z = 1
ax + by + z = 0
has no solution, then S is :
Solutions · 1
Official solution
\[\left| {11a1ab111 } \right| = 0\]
\[ \Rightarrow \] 1 [a -- b] -- 1 [1 -- a] + 1 [b -- a2] = 0
\[ \Rightarrow \] (a - 1)2 = 0
\[ \Rightarrow \] a = 1
For a = 1, the equations become
x + y + z = 1
x + y + z = 1
x + by + z = 0
These equations give no solution for b = 1
\[ \Rightarrow \] S is singleton set.