Home
Class 12
MATHS
Using properties of determinants. Prove ...

Using properties of determinants. Prove that `|xx^2 1+p x^3y y^2 1+p y^3z z^2 1+p z^3|=(1+p x y z)(x-y)(y-z)(z-x)` , where p is any scalar.

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    NCERT GUJARATI|Exercise EXERCISE 4.6|16 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT GUJARATI|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 5|23 Videos

  • DIFFERENTIAL EQUATIONS

    NCERT GUJARATI|Exercise MISCELLANEOUS EXERCISE|18 Videos

Similar Questions

Explore conceptually related problems

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 properties of determinants in Exercise 1 to 6, evaluate |{:(3x,-x+y,-x+z),(x-y,3y,z-y),(x-z,y-z,3z):}|

Using the properties of determinants in Exercise 1 to 6, evaluate |{:(a+x,y,z),(x,a+y,z),(x,y,a+z):}|

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

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 x,y,z are different and Delta=|{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^2,1+z^3):}| =0 then show that 1+xyz=0

Prove that the lines x=2 (y-1)/(3) = (z-2)/(1) and x = (y-1)/(1) = (z+1)/(3) are skew lines.

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)

NCERT GUJARATI-DETERMINANTS -Miscellaneous Exercises on Chapter 4
  1. Prove that the determinant Delta =|{:(x,,sin0,,cos 0),(-sin 0,,-x,...

    Text Solution

    |

  2. Without expanding the determinant, prove that {:[( a, a ^(2), bc ),( ...

    Text Solution

    |

  3. Evaluate |cosalphacosbetacosalphasinbeta-sinalpha-sinbetacosbeta0sinal...

    Text Solution

    |

  4. If a, b and c are real numbers, and Delta=|b+cc+a a+b c+a a+bb+c a+bb+...

    Text Solution

    |

  5. Solve the equation |x+a xxxx+a xxxx+a|=0, a!= 0

    Text Solution

    |

  6. Prove that : (i) |{:(a,c,a+c),(a+b,b,a),(b,b+c,c):}|=2 abc (ii) Pr...

    Text Solution

    |

  7. If A-^1=[3-1 1-15 6-5 5-2 2] and B=[1 2-2-1 3 0 0-2 1] , find (A B)^(-...

    Text Solution

    |

  8. Evaluate |[x,y,x+y],[y,x+y,x],[x+y,x,y]|

    Text Solution

    |

  9. Evaluate the following: |[1,x,y],[1, x+y, y],[1, x, x+y]|

    Text Solution

    |

  10. Using peoperties of determinants in questions 11 to 15, prove that : ...

    Text Solution

    |

  11. Using properties of determinants. Prove that |xx^2 1+p x^3y y^2 1+p y^...

    Text Solution

    |

  12. Show that: |(3a,-a+b,-a+c),(-b+a,3b,-b+c),(-c+a,-c+b,3c)|=3(a+b+c)(a b...

    Text Solution

    |

  13. Show that |1 1+p1+p+q2 3+2p1+3p+2q3 6+3p 106 p+3q|=1.

    Text Solution

    |

  14. Without expanding, show that the value of each of the determinants is ...

    Text Solution

    |

  15. Solve the system of equations2/x+3/y+(10)/z=44/x-6/y+5/z=16/x+9/y-(20)...

    Text Solution

    |

  16. Choose the correct answer in questions 17 to 19: If a, b, c are in ...

    Text Solution

    |

  17. Choose the correct answer in questions 17 to 19: If x, y, z are non...

    Text Solution

    |

  18. Let A = [(1,sin theta,1),(- sin theta,1,sin theta),(-1,-sin theta,1)],...

    Text Solution

    |