If for the system of linear equations having infinite solutions \(\begin{aligned}& (\lambda-4) x+(\lambda-2) y+\lambda z…
Q1 FREE PREVIEW
PYQIf for the system of linear equations having infinite solutions
\(\begin{aligned}& (\lambda-4) x+(\lambda-2) y+\lambda z=0 \\& 2 x-3 y+5 z=0 \\& x+2 y+6 z=0\end{aligned}\)
then \(\lambda^2+\lambda\) is
✓ Correct answer: b)
\(\frac{9}{2}\)
Explanation
\(\begin{aligned}&\text { Given system has infinite solution }\\&& \Rightarrow\left|\begin{array}{ccc}\lambda-4 & \lambda-2 & \lambda \\2 & -3 & 5 \\1 & 2 & 6\end{array}\right|=0 \\& \Rightarrow(\lambda-4)(-28)-(\lambda-2) 7+\lambda \times 7=0 \\& \Rightarrow-4(\lambda-4)-(\lambda-2)+d=0 \\& \Rightarrow-4 \lambda+16-\lambda+2+\lambda=0 \\& =-4 \lambda=-18 \quad\lambda=\frac{9}{2}\end{aligned}\)
Practice more JEE Maths PYQs
See every question on Matrices, or browse the full JEE question bank.
See all questions on Matrices →