The system of equations - kx + 3y - 14z = 25 - 15x + 4y - kz = 3 - 4x + y + 3z = 4 is cons…

Question

The system of equations
$- kx + 3y - 14z = 25$
$- 15x + 4y - kz = 3$
$- 4x + y + 3z = 4$
is consistent for all k in the set

Accepted Answer

The system may be inconsistent if

$$\left| {\begin{pmatrix} { - k} & 3 & { - 14}  \
   { - 15} & 4 & { - k}  \
   { - 4} & 1 & 3  \

\end{pmatrix} } \right| = 0 \Rightarrow k = \, \pm \,11$$

Hence if system is consistent then $$k \in R - \{ 11, - 11\} $$.

Solutions · 1