The value of k $\in$R, for which the following system of linear equations
3x $-$ y + 4z = 3,
x + 2y $-$ 3z = $-$2
6x + 5y + kz = $-$3,
has infinitely many solutions, is :
Solution
$$\left| {\matrix{
3 & { - 1} & 4 \cr
1 & 2 & { - 3} \cr
6 & 5 & k \cr
} } \right| = 0$$<br><br>$\Rightarrow$ 3(2k + 15) + K + 18 $-$ 28 = 0<br><br>$\Rightarrow$ 7k + 35 = 0 <br><br>$\Rightarrow$ k = $-$ 5
About this question
Subject: Mathematics · Chapter: Matrices and Determinants · Topic: Types of Matrices and Operations
This question is part of PrepWiser's free JEE Main question bank. 274 more solved questions on Matrices and Determinants are available — start with the harder ones if your accuracy is >70%.