Home
Class 12
MATHS
If Delta=|{:(1,x,x^(2)),(1,y,y^(2)),(1,z...

If `Delta=|{:(1,x,x^(2)),(1,y,y^(2)),(1,z,z^(2)):}|`, `Delta_(1)=|{:(1,1,1),(yz,zx,xy),(x,y,z):}|`, then prove that `Delta+Delta_(1)=0`

Text Solution

AI Generated Solution

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Exercise 4(a) (SHORT ANSWER TYPE QUESTIONS)|20 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Exercise 4(b) (SHORT ANSWER TYPE QUESTIONS)|11 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Examples (FREQUENCY ASKED QUESTIONS)|28 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

  • DIFFERENTIAL EQUATIONS

    MODERN PUBLICATION|Exercise CHAPTER TEST (9)|12 Videos

Similar Questions

Explore conceptually related problems

Prove the following : |(1,x,x^(2)-yz),(1,y,y^(2)-zx),(1,z,z^(2)-xy)|=0 .

Prove that |{:(ax,,by,,cz),(x^(2),,y^(2),,z^(2)),(1,,1,,1):}|=|{:(a,,c,,c),(x,,y,,z),(yz,,xz,,xy):}|

Knowledge Check

  • If Delta=|(1,x,x^2),(1,y,y^2),(1,z,z^2| and Delta_1=|(1,1,1),(yz,zx,xy),(x,y,z)| , then the value of Delta+Delta_1 is

    A
    `Delta*Delta_1`
    B
    1
    C
    0
    D
    None of these

  • Let Delta_(1)=|{:(Ax,x^(2),1),(By,y^(2),1),(Cz,z^(2),1):}| and Delta_(2)=|{:(A,B,C),(x,y,z),(yz,zx,xy):}| , then :

    A
    `Delta_(1)=-Delta`
    B
    `Delta ne Delta_(1)`
    C
    `Delta-Delta_(1)=0`
    D
    None of these

  • The value of |{:(x,x^2-yz,1),(y,y^2-zy,1),(z,z^2-xy,1):}| is

    A
    1
    B
    -1
    C
    0
    D
    None

    • Similar Questions

    Explore conceptually related problems

    If Delta_1 = |[1,1,1] , [x^2, y^2, z^2] , [x,y,z]| and Delta_2=|[1,1,1] , [yz, zx, xy] , [x,y,z]| then without expanding show that Delta_1= Delta_2

    |(ax,by,cz),(x^2,y^2,z^2),(1,1,1)|=|(a,b,c),(x,y,z),(yz,zx,xy)|

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

    Show that Delta =Delta_(1) , where Delta = |[Ax,x^(2), 1],[By, y^(2), 1],[Cz, z^(2),1]| "and "Delta_(1) = |[A,B, C],[x, y, z],[zy, zx,xy]|

    |[yz,x,x^(2)],[zx,y,y^(2)],[xy,z,z^(2)]|=|[1,x^(2),x^(3)],[1,y^(2),y^(3)],[1,z^(2),z^(3)]|

    Home
    Profile