If the system of linear equations
$2x + 3y - z = - 2$
$x + y + z = 4$
$x - y + |\lambda |z = 4\lambda - 4$
where, $\lambda$ $\in$ R, has no solution, then
Solution
<p>$$\Delta = \left| {\matrix{
2 & 3 & { - 1} \cr
1 & 1 & 1 \cr
1 & { - 1} & {|\lambda |} \cr
} } \right| = 0 \Rightarrow |\lambda | = 7$$</p>
<p>But at $\lambda = 7,\,{D_x} = {D_y} = {D_z} = 0$</p>
<p>${P_1}:2x + 3y - z = - 2$</p>
<p>${P_2}:x + y + z = 4$</p>
<p>${P_3}:x - y + |\lambda |z = 4\lambda - 4$</p>
<p>So clearly $5{P_2} - 2{P_1} = {P_3}$, so at $\lambda = 7$, system of equation is having infinite solutions.</p>
<p>So $\lambda = - 7$ is correct answer.</p>
About this question
Subject: Mathematics · Chapter: Matrices and Determinants · Topic: Types of Matrices and Operations
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