Home
Class 12
MATHS
show that [((x+y)^2 , zx , zy),( zx, (...

show that
`[((x+y)^2 , zx , zy),( zx, (z+y)^2 ,xy),(zy,xy,(z+x)^2)]=2xyz (x +y+z)^3`

Text Solution

Verified by Experts

The correct Answer is:
`2xyz(x+y+z)^3`
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Short Answer Type Questions)|17 Videos

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Long Answer Type Questions)|6 Videos

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise Textbook based MCQs|42 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    KUMAR PRAKASHAN|Exercise Practice Paper - 5 (Section-D)|4 Videos

  • INTEGRALS

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER-7 (SECTION-D)|2 Videos

Similar Questions

Explore conceptually related problems

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(x+y+2z,x,y),(z,y+z+2x,y),(z,x,z+x+2y):}|=2(x+y+z)^3

If Delta = abs{:(x+y+z^(2) , x^(2) + y+ z, x+y^(2) + z),(z^2, x^2, y^2),(x+y,y+z,x+z):} , (where ( x ne y ne z) x, y, z in R- {0} ) then Delta= ........

Prove that |{:(x^2,y^2,z^2),((x+1)^2,(y+1)^2,(z+1)^2),((x-1)^2,(y-1)^2,(z-1)^2):}|=-4(x-y)(y-z)(z-x)

Verify that x ^(3) + y ^(3) + z ^(3) - 3xyz =1/2 (x + y + z) [(x-y)^(2) + (y-z) ^(2) + (z-x) ^(2) ]

Using properties of determinants in Exercise 11 to 15 prove that |{:(x,x^2,1+px^3),(y,y^2,1+py^3),(z,z^2,1+pz^3):}|=(1+pxyz)(x-y)(y-z)(z-x)

Using the proprties of determinants in Exercise 7 to 9, prove that |{:(y^2z^2,yz,y+z),(x^2z^2,zx,z+x),(x^2y^2,xy,x+y):}|=0

The number of positive integral solutions of the equation |(x^3+1,x^2y,x^2z),(xy^2,y^3+1,y^2z),(xz^2,z^2y,z^3+1)|=11 is

(a) If x + y + z=0, show that x ^(3) + y ^(3) + z ^(3)= 3 xyz. (b) Show that (a-b) ^(3) + (b-c) ^(3) + (c-a)^(3) =3 (a-b) (b-c) (c-a)

KUMAR PRAKASHAN-DETERMINANTS -Textbook Illustrations for Practice work
  1. If x,y,z are different and Delta=|{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z...

    Text Solution

    |

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

    Text Solution

    |

  3. Find the area of the triangle whose vertices are (3,8),(-4,2) and (5,1...

    Text Solution

    |

  4. Find the equation of the line joining A(1,3) and B(0,0) using determin...

    Text Solution

    |

  5. Find the minor of elements 6 in the determinant Delta=|{:(1,2,3),(4,...

    Text Solution

    |

  6. Find minors and cofactors of all the elements of the determinant |{:(1...

    Text Solution

    |

  7. Find minors and cofactors of the elements a(11),a(21) in the determina...

    Text Solution

    |

  8. Find minors and cofactors of the elements of the determinant |{:(2,-3,...

    Text Solution

    |

  9. Find adj A for A = {:[( 2,3),( 1,4) ]:}

    Text Solution

    |

  10. If A=[{:(1,3,3),(1,4,3),(1,3,4):}] , then verify that A adjA=|A|I. Als...

    Text Solution

    |

  11. If A=[{:(2,3),(1,-4):}] and B=[{:(1,-2),(-1,3):}] then verify that (AB...

    Text Solution

    |

  12. Show that the matrix A=[{:(2,3),(1,2):}] satisfies the equation A^2-4A...

    Text Solution

    |

  13. Solve the system of equations {:(2x+5y=1),(3x+2y=7):},

    Text Solution

    |

  14. Solve system of linear equations , using matrix method if exists 4x-...

    Text Solution

    |

  15. The sum of three numbrs is 6. If we multiply third number by 3 and add...

    Text Solution

    |

  16. If a,b,c are positive and unequal, show that value of the determinant ...

    Text Solution

    |

  17. If a,b,c are in A.P find value of |{:(2y+4,5y+7,8y+a),(3y+5,6y+8,9y+...

    Text Solution

    |

  18. show that [((x+y)^2 , zx , zy),( zx, (z+y)^2 ,xy),(zy,xy,(z+x)^2)]=2...

    Text Solution

    |

  19. Solve following system using matrix x-y+2z =1 , 2y -3z =1, 3x...

    Text Solution

    |

  20. Prove that |{:(a+bx,c+dx,p+qx),(ax+b,cx+d,px+q),(mu,vartheta,omega):}|...

    Text Solution

    |