Home
Class 12
MATHS
Using properties of determinants, prove ...

Using properties of determinants, 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)`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    PSEB|Exercise Exercise|101 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    PSEB|Exercise Exercise|151 Videos

  • DIFFERENTIAL EQUATIONS

    PSEB|Exercise Exercise|116 Videos

Similar Questions

Explore conceptually related problems

Using the properties of determinant, show that : |[1,x+y,x^2+y^2],[1,y+z,y^2+z^2],[1,z+x,z^2+x^2]| = (x-y)(y-z)(z-x)

By using properties of determinants, show that : |[x+y+2z,x,y],[z,y+z+2x,y],[z,z,z+x+2y]| = 2(x+y+z)^3

Using the properties of determinants, show that : |[[x, y, z],[x^2, y^2, z^2],[x,y,z]]|= 0 .

Using the properties of determinants, show that : |[[x^2, y^2, z^2],[yz, zx, xy],[x,y,z]]|= (x-y)(y-z)(z-x)(xy+yz+zx) .

Using properties of determinants , prove that |(x^2+1,xy,zx),(xy,y^2+1,yz),(zx,yz,z^2+1)|=1+x^2+y^2+z^2

Using the properties of determinants, prove that : |[[a+x,y,z],[x,a+y,z],[x,y,a+z]]|=a^2(a+x+y+z)

Using properties of determinants, prove that : {:|((x+y)^2,zx,zy),(zx,(z+y)^2,xy),(zy,xy,(z+x)^2)|=2xyz(x+y+z)^3

Show that |(1,x^2,x^3),(1,y^2,y^3),(1,z^2,z^3)| = (x-y),(y-z)(z-x)(xy+yz+zx)

Prove that |[[x,y,z],[x^2,y^2,z^2],[x^3,y^3,z^3]]|= xyz (x-y)(y-z)(z-x)

PSEB-DETERMINANTS-Exercise
  1. Prove that the determinant |[x,sintheta,costheta],[-sintheta,-x,1],[co...

    Text Solution

    |

  2. Without expanding the determinant, prove that |[a,a^2,bc],[b,b^2,ca],[...

    Text Solution

    |

  3. Evaluate |[cosalphacosbeta,cosalphasinbeta,-sinalpha],[-sinbeta,cosbet...

    Text Solution

    |

  4. If a, b and c are real numbers, and triangle = |[b+c,c+a,a+b],[c+a,a+b...

    Text Solution

    |

  5. Solve the equation |[x+a,x,x],[x,x+a,x],[x,x,x+a]| = 0 a ne 0

    Text Solution

    |

  6. Prove that: |[a^2,bc,ac+c^2],[a^2+ab,b^2,ac],[ab,b^2+bc,c^2]|=4a^2b^2c...

    Text Solution

    |

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

    Text Solution

    |

  8. Let A = [[1,-2,1],[-2,3,1],[1,1,5]] Verify that [adj A]^-1 = adj (A^-1...

    Text Solution

    |

  9. Let A = [[1,-2,1],[-2,3,1],[1,1,5]] Verify that [adj A]^-1 = adj (A^-1...

    Text Solution

    |

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

    Text Solution

    |

  11. Evaluate |[1,x,y],[1,x+y,y],[1,x,x+y]|

    Text Solution

    |

  12. Using properties of determinants, prove that: |[alpha,alpha^2,beta+gam...

    Text Solution

    |

  13. Using properties of determinants, prove that: |[x,x^2,1+px^3],[y,y^2,1...

    Text Solution

    |

  14. Using properties of determinants, prove that: |[3a,-a+b,-a+c],[-b+a,3b...

    Text Solution

    |

  15. Prove that: |[1,1+p,1+p+q],[2,3+2p,4+3p+2q],[3,6+3p,10+6p+3q]|=1

    Text Solution

    |

  16. Using properties of determinants, prove that: |[sinalpha,cosalpha,cos(...

    Text Solution

    |

  17. Solve the system of equations: 2/x+3/y+10/z = 4, 4/x-6/y+5/z = 1, 6/x+...

    Text Solution

    |

  18. If a, b, c, are in A.P, then the determinant |[x+2,x+3,x+2a],[x+3,x+4,...

    Text Solution

    |

  19. If x. y, z are non- real number", then the inverse of matrix A = [[x,0...

    Text Solution

    |

  20. Let A = [[1,sintheta,1],[-sintheta,1,sintheta],[-1,-sintheta,1]], wher...

    Text Solution

    |