Home
Class 12
MATHS
If Delta=|{:(,x,2y-z,-z),(,y,2x-z,-z),(,...

If `Delta=|{:(,x,2y-z,-z),(,y,2x-z,-z),(,y,2y-z,2x-2y-z):}|`,then

A

x–y is a factor of `Delta`

B

`(x-y)^(2)` is a factor of `Delta`

C

`(x-y)^(3)` is a factor of `Delta`

D

`Delta` is independent of z

Text Solution

Verified by Experts

The correct Answer is:
A, B
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    MOTION|Exercise EXERCISE-3|36 Videos
  • DETERMINANTS

    MOTION|Exercise EXERCISE-4 (LEVEL-I)|13 Videos
  • DETERMINANTS

    MOTION|Exercise EXERCISE-2 (LEVEL-I)|9 Videos
  • DEFINITE INTEGRATION

    MOTION|Exercise EXERCISE -4 LEVEL-II|33 Videos
  • DIFFERENTIABILITY

    MOTION|Exercise Exercise - 4 | Level-I Previous Year | JEE Main|15 Videos

Similar Questions

Explore conceptually related problems

Prove that : |{:(x-y-z,2x,2x),(2y,y-z-x,2y),(2z,2z,z-x-y):}|

x-y+z=1 2x+y-z=2 x-2y-z=4

Prove that |{:(x,y,z),(x^2,y^2,z^2),(yz,zy,xy):}|=|{:(1,1,1),(x^2,y^2,z^2),(x^3,y^3,z^3):}|=(y-z)(z-x)(x-y)(yz+zy+xy)

If x,y,z in R & Delta =|(x,x+y,x+y+z),(2x,5x+2y,7x+5y+2z),(3x,7x+3y,9x+7y+3z)|=-16 then the value of x is

Prove the following : |{:(x,x^(2),y+z),(y,y^(2),z+x),(z,z^(2),x+y):}|=(y-z)(z-x)(x-y)(x+y+z)

Prove that : |{:(x+y+2z,x,y),(z,y+z+2x,y),(z,x,x+a+2y):}|=2(x+y+)^(3)

Prove that : =2|{:(1,1,1),(x,y,rz),(x^(2),y^(2),z^(2)):}|=(x-y)(y-z)(z-x)

Prove: |(2y, y-z-x,2y),(2z,2z, z-x-y),( x-y-z,2x,2x)|=(x+y+z)^3