Matrices and Determinants — Page 28 | JEE Mathematics

JEE Mathematics · 271 questions · Page 28 of 28 · Click an option or "Show Solution" to reveal answer

Q271

If the system of linear equations x + y + 3z = 0 x + 3y + k2z = 0 3x + y + 3z = 0 has a non-zero solution (x, y, z) for some k

\in

R, then x +

\left( {{y \over z}} \right)

is equal to :

A 9

B 3

C -9

D -3

Correct Answer

Option D

Solution

x + y + 3z = 0 .....(i) x + 3y + k2z = 0 .........(ii) 3x + y + 3z = 0 ......(iii)

\left| \begin{array}{lll}1 & 1 & 3 \\ 1 & 3 & {{k^2}} \\ 3 & 1 & 3 \end{array} \right|

= 0 $\Rightarrow$ 9 + 3 + 3k2 – 27 – k2 – 3 = 0 $\Rightarrow$ k2 = 9 Perform (i) – (iii), –2x = 0 $\Rightarrow$ x = 0 Now from (i), y + 3z = 0 $\Rightarrow$

{y \over z} = - 3

$\therefore$ x +

\left( {{y \over z}} \right)

= -3