The system of equations [5x+ y+3z=12, 2x-y+z=4, 100x-47y+ z=212] has no solution if:

Question

The system of equations
$$5x+\lambda y+3z=12,\qquad 2x-y+z=4,\qquad 100x-47y+\mu z=212$$
has no solution if:

Accepted Answer

The coefficient determinant $D=0$ gives $\lambda=17$.

With $\lambda=17$, checking $D_z
e0$ requires $\mu
e18$ for the system to be inconsistent (no solution) rather than have infinitely many solutions.

So the condition is $\lambda=17,\ \mu
e18$ --- Option B.

Solutions · 1