The system of equations
$- kx + 3y - 14z = 25$
$- 15x + 4y - kz = 3$
$- 4x + y + 3z = 4$
is consistent for all k in the set
Solution
<p>The system may be inconsistent if</p>
<p>$$\left| {\matrix{
{ - k} & 3 & { - 14} \cr
{ - 15} & 4 & { - k} \cr
{ - 4} & 1 & 3 \cr
} } \right| = 0 \Rightarrow k = \, \pm \,11$$</p>
<p>Hence if system is consistent then $k \in R - \{ 11, - 11\}$.</p>
About this question
Subject: Mathematics · Chapter: Matrices and Determinants · Topic: Types of Matrices and Operations
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