For which of the following ordered pairs (\[\mu \], \[\delta \]),
the system of linear equations
x + 2y + 3z = 1
3x + 4y + 5z = \[\mu \]
4x + 4y + 4z = \[\delta \]
is inconsistent ?
Solutions · 1
Official solution
For inconsistent system we need
\[\Delta \] = 0 and atleast one of \[\Delta \]x, \[\Delta \]y, \[\Delta \]z \[ \ne \] 0
\[ \therefore \] \[\Delta \] = \[\left| {134244354 } \right|\] = 0
\[\Delta \]x = \[\left| {1μδ244354 } \right|\]
= (-4) - 2(\[\mu \] - 5\[\delta \]) + 3(4\[\mu \] - 4\[\delta \])
\[ \Rightarrow \] 2\[\mu \] \[ \ne \] \[\delta \] + 2 ....(1)
Only (\[\mu \], \[\delta \]) = (4, 3) does satisfy the equation (1).