Home
Class 12
MATHS
Prove that: |[a^2,bc,ac+c^2],[a^2+ab,b^2...

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

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    MODERN PUBLICATION|Exercise EXERCISE|326 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise EXERCISE|588 Videos

  • EXCLUSIVELY FOR JEE(ADVANCED)

    MODERN PUBLICATION|Exercise EXERCISE|38 Videos

Similar Questions

Explore conceptually related problems

Prove that: |[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]|=|[a^2+1,b^2,c^2],[a^2,b^2+1,c^2],[a^2,b^2,c^2+1]|=1+a^2+b^2+c^2

Prove that: |[-a^2, ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]|=4a^2b^2c^2

Using the properties of determinant, show that : |[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]| = 1+a^2+b^2+c^2

|[x^2+a^2,ab,ac] , [ab,x^2+b^2,bc] , [ac,bc,x^2+c^2]|=

Prove that |[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-ab]|= 0

Without expanding the determinant, prove that |[a,a^2,bc],[b,b^2,ca],[c,c^2,ab]| = |[1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3]|

Using the properties of determinants show that : |[[-bc,b^2+bc,c^2+bc],[a^2+ac,-ac,c^2+ac],[a^2+ab,b^2+ab,-ab]]|=(ab+bc+ca)^3

Without expanding, prove the following |(0,ab^2,ac^2),(a^2b,0,bc^2),(a^2b,b^2c,0)|=2a^3b^3c^3

MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. 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

    |

  2. Let A be a square matrix of order 3xx3, then prove that |kA|=k|A|.

    Text Solution

    |

  3. If any two rows (or columns) of a determinant are identical, the value...

    Text Solution

    |

  4. Answer in one word. {:|(3,1,6),(5,2,10),(7,4,14)|

    Text Solution

    |

  5. If A is a square matrix of order 3 and |3A| = k|A|, then write the val...

    Text Solution

    |

  6. Write the value of the following determinant abs{:(a-b, b-c, c-a),(b-c...

    Text Solution

    |

  7. Use properties of determinants ot evaluate: {:|(2,a,abc),(2,b,bca),(...

    Text Solution

    |

  8. Use properties of determinants ot evaluate: {:|(x+y,y+z,z+x),(z,x,y)...

    Text Solution

    |

  9. Evaluate |[102,18,36],[1,3,4],[17,3,6]|

    Text Solution

    |

  10. Use properties of determinants ot evaluate: {:|(2,3,1),(4,6,2),(1,3,...

    Text Solution

    |

  11. Use properties of determinants ot evaluate: {:|(2,3,5),(261,592,127)...

    Text Solution

    |

  12. Show that x=1 is a root of the equation: {:|(x+1,2x,-11),(2x,x+1,-4...

    Text Solution

    |

  13. If p,q,r ar in A.P. write the value of : {:|(x+1,x+2,x+2p),(x+2,x+3,...

    Text Solution

    |

  14. Without expanding, prove that the following determinant vanishes. |...

    Text Solution

    |

  15. Without actual expansion, prove that the following determinants vanish...

    Text Solution

    |

  16. Without actual expansion, prove that the following determinants vanish...

    Text Solution

    |

  17. Without actual expansion, prove that the following determinants vanish...

    Text Solution

    |

  18. Without actual expansion, prove that the following determinants vanish...

    Text Solution

    |

  19. Without actual expansion, prove that the following determinants vanish...

    Text Solution

    |

  20. Without expanding, prove that Delta = abs{:(x+y, y + z, z+ x),(z, x ,...

    Text Solution

    |

  21. Without expanding, prove that : |{:(1, bc, a(b+ c) ),(1, ca, b ( c+ a)...

    Text Solution

    |