SATHEE: Matrices and Determinants 2 Question 18

Matrices and Determinants 2 Question 18

20. The determinant $| \begin{matrix} x p + y & x & y \\ y p + z & y & z \\ 0 & x p + y & y p + z \end{matrix} | = 0$ , if

(a) $x, y, z$ are in $AP$

(b) $x, y, z$ are in GP

(d) $x y, y z, z x$ are in AP

Show Answer

Answer:

Correct Answer: 20. (b)

Solution:

Given, $| \begin{matrix} x p + y & x & y \\ y p + z & y & z \\ 0 & x p + y & y p + z \end{matrix} | = 0$

Applying $C_{1} \to C_{1} - (p C_{2} + C_{3})$

$\begin{aligned} \Rightarrow | \begin{array}{c} 0 & x & y \\ 0 & y & z \\ - (x p^{2} + y p + y p + z) & x p + y & y p + z \end{array} | = 0 \\ \Rightarrow - (x p^{2} + 2 y p + z) (x z - y^{2}) = 0 \end{aligned}$

$∴ Either x p^{2} + 2 y p + z = 0 or y^{2} = x z$

$\Rightarrow x, y, z$ are in GP.

Play Store

App Store

Ask SATHEE

Welcome to SATHEE !
Select from 'Menu' to explore our services, or ask SATHEE to get started. Let's embark on this journey of growth together! 🌐📚🚀🎓

I'm relatively new and can sometimes make mistakes.
If you notice any error, such as an incorrect solution, please use the thumbs down icon to aid my learning.
To begin your journey now, click on "I understand".

Matrices and Determinants 2 Question 18

20. The determinant |xp+yxyyp+zyz0xp+yyp+z|=0, if

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu

20. The determinant $| \begin{matrix} x p + y & x & y \\ y p + z & y & z \\ 0 & x p + y & y p + z \end{matrix} | = 0$ , if