Home
Class 12
MATHS
[[x, x^2, yz],[y, y^2, zx],[z, z^2, xy]]...

`[[x, x^2, yz],[y, y^2, zx],[z, z^2, xy]]=(x-y)(y-z)(z-x)(xy+yz+zx)`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

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

  • DETERMINANTS

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

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Exercise 4(b) (LONG ANSWER TYPE QUESTIONS (I))|19 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

[[x,x^(2),yzy,y^(2),zxz,z^(2),xy]]=(x-y)(y-z)(z-x)(xy+yz+zx)

By using properties of determinants.Show that: det[[x,x^(2),yzy,y^(2),zxz,z^(2),xy]]=(x-y)(y-z)(z-x)(xy+yz+zx)

Using the properties of determinants, show that: abs((x,x^2,yz),(y,y^2,xz),(z,z^2,xy))=(x−y)(y−z)(z−x)(xy+yz+zx)

xquad x ^ (2), y2yquad y ^ (2), 2xz, z ^ (2), xy] | = (xy) (yz) (zx) (xy + yz + 2x)

Determinant , form (x-y)(y-z)(z-x)(xy+yz+zx), of

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

Show that |[yz-x^2, zx-y^2, xy-y^2] , [zx-y^2, xy-z^2, yz-x^2] , [xy-z^2, yz-x^2, zx-y^2]|= |[r^2, u^2, u^2] , [u^2, r^2, u^2] , [u^2, u^2, r^2]| where r^2 = x^2+y^2+z^2 and u^2= xy+yz+zx

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

Simplify- (x-y)/(xy)+(y-z)/(yz)+(z-x)/(zx)

Prove that |[x,y,z] , [x^2, y^2, z^2] , [yz, zx, xy]| = |[1,1,1] , [x^2, y^2, z^2] , [x^3, y^3, z^3]|

MODERN PUBLICATION-DETERMINANTS-Exercise 4(b) (LONG ANSWER TYPE QUESTIONS (II))
  1. |[1+a^2-b^2,2ab,-2b],[2ab,1-a^2+b^2,2a],[2b,-2a,1-a^2-b^2]|=(1+a^2+b^2...

    Text Solution

    |

  2. Prove the following : |{:(x,y,z),(x^(2),y^(2),z^(2)),(x^(3),y^(3),z^...

    Text Solution

    |

  3. [[x, x^2, yz],[y, y^2, zx],[z, z^2, xy]]=(x-y)(y-z)(z-x)(xy+yz+zx)

    Text Solution

    |

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

    Text Solution

    |

  5. Prove that |{:(b+c, c+a, a+b),(c+a, a+b,b+c),(a+b, b+c, c+a):}| =2(...

    Text Solution

    |

  6. Using properties of determinants, prove the following: |xx+y x+2y\...

    Text Solution

    |

  7. |[b+c, a,a] , [b,c+a,b] , [c,c,a+b]|=4abc

    Text Solution

    |

  8. Prove the following : |{:(2ab,a^(2),b^(2)),(a^(2),b^(2),2ab),(b^(2),...

    Text Solution

    |

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

    Text Solution

    |

  10. For any scalar p prove that =|xx^2 1+p x^3y y^2 1+p y^3z z^2 1+p z^3|=...

    Text Solution

    |

  11. |(x+y+z,-z,-y),(-z,x+y+z,-x),(-y,-x,x+y+z)|=2(x+y)(y+z)(z+x)

    Text Solution

    |

  12. Prove: |2y y-z-x2y2z2z z-x-y x-y-z2x2x|=(x+y+z)^3

    Text Solution

    |

  13. |(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|

    Text Solution

    |

  14. Show that: |3a-a+b-a+c-b+a3b-b+c-c+a-c+b3c|=3(a+b+c)(a b+b c+c a)dot

    Text Solution

    |

  15. Using properties of determinants. Find the value of 'x' |(4-x,4+x,4+...

    Text Solution

    |

  16. Solve: |a+x a-x a-x a-x a+x a-x a-x a-x a+x|=0

    Text Solution

    |

  17. Prove that |[x, sintheta, costheta],[-sintheta, -x, 1],[costheta, 1, ...

    Text Solution

    |

  18. Prove that |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}| =abc (1+(1)/(a)+(1)/...

    Text Solution

    |

  19. Prove that : |{:((y+z)^(2),x^(2),x^(2)),(y^(2),(x+z)^(2),y^(2)),(z^(2)...

    Text Solution

    |

  20. Prove that | ((b+c)^2, a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2)|=2...

    Text Solution

    |