If the system of linear equations
x + ay + z = 3
x + 2y + 2z = 6
x + 5y + 3z = b
has no solution, then :
Solutions · 1
Official solution
As the given system of equations has no solution then
\[\Delta \] = 0 and at least one of \[\Delta \]1, \[\Delta \]2 and \[\Delta \]2 should not be zero.
\[ \therefore \] \[\Delta \] = \[\left| {111a25123 } \right| = 0\]
\[ \Rightarrow \] - a - 1 = 0
\[ \Rightarrow \] a = - 1
\[\Delta \]2 = \[\left| {11136b123 } \right| \ne 0\]
\[ \Rightarrow \] b \[ \ne \] 0