Let [ ] be a real number for which the system of linear equations x + y + z = 6, 4x + [ ]y…

Question

Let $$\lambda $$ be a real number for which the system of linear equations x + y + z = 6, 4x + $$\lambda $$y -- $$\lambda $$z = $$\lambda $$ -- 2,
3x + 2y -- 4z = -- 5 has infinitely many solutions. Then $$\lambda $$ is a root of the quadratic equation:

Accepted Answer

$$\Delta  = 0$$

$$\left| {\begin{pmatrix} 1 & 1 & 1  \
   4 & \lambda  & { - \lambda }  \
   3 & 2 & { - 4}  \

\end{pmatrix} } \right| = 0$$

On solving we get $$\lambda $$ = 3

Solutions · 1