Home
Class 12
MATHS
Using the properties of determinant, sho...

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`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    PRADEEP PUBLICATION|Exercise EXERCISE|342 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    PRADEEP PUBLICATION|Exercise EXERCISE|788 Videos

  • DIFFERENTIAL EQUATIONS

    PRADEEP PUBLICATION|Exercise EXERCISE|507 Videos

Similar Questions

Explore conceptually related problems

By using properties of determinants, show that : |[1,a,a^2],[1,b,b^2],[1,c,c^2]| = (a-b)(b-c)(c-a)

Using the properties of determinant, show that : |[1,a+b,a^2+b^2],[1,b+c,b^2+c^2],[1,c+a,c^2+a^2]| = (a-b)(b-c)(c-a)

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

Using the properties of determinants show that : |[[1, a^2+bc, a^3],[1,b^2+ac,b^3],[1,c^2+ab,c^3]]|=(a-b)(b-c)(c-a)(a^2+b^2+c^2)

Using the properties of determinants show that : |[[1,1,1],[a^2,b^2,c^2],[a^3,b^3,c^3]]|=(a-b)(b-c)(c-a)(ab+bc+ca) .

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

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

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

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

Using the properties of determinants, show that |(1+a,1,1),(1,1+b,1),(1,1,1+c)|=abc+bc+ca+ab

PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. Using the properties of determinant, show that :|[a^2+1,ab,ac],[ab,b^2...

    Text Solution

    |

  2. If A = [(13,-10),(7,87)], write the following submatrices of A. A12

    Text Solution

    |

  3. If A = [(13,-10),(7,87)], write the following submatrices of A. A22

    Text Solution

    |

  4. If A = [(a,h,g),(h,b,f),(g,f,c)], find the submatrix of A obtained by ...

    Text Solution

    |

  5. If A = [(a,h,g),(h,b,f),(g,f,c)], find the submatrix of A obtained by ...

    Text Solution

    |

  6. If A = [(a,h,g),(h,b,f),(g,f,c)], find the submatrix of A obtained by ...

    Text Solution

    |

  7. If A = [(a,h,g),(h,b,f),(g,f,c)], find the submatrix of A obtained by ...

    Text Solution

    |

  8. Find the minors and cofactos of each entry of the first column of the ...

    Text Solution

    |

  9. Find the minors and cofactos of each entry of the first column of the ...

    Text Solution

    |

  10. Find the minors and cofactos of each entry of the first column of the ...

    Text Solution

    |

  11. Find the minors and cofactos of each entry of the first column of the ...

    Text Solution

    |

  12. Evaluate the following determinants: {:|(-2,3),(4,-9)|

    Text Solution

    |

  13. Evalate the following determinants: |(1//2, 8),(4,2)|

    Text Solution

    |

  14. Evaluate the following determinants: |(a+ib , - c + id),(c+id, a-ib)...

    Text Solution

    |

  15. Evaluate the following determinants: |(3x, x-7),(x+1,5x+1)|

    Text Solution

    |

  16. Show that |(sin10^@, - cos10^@),(sin80^@, cos80^@)| = 1

    Text Solution

    |

  17. Show that {:|(cos15^@, sin15^@),(sin75^@, cos75^@)|:}= 0

    Text Solution

    |

  18. Evaluate |(x,x+1),(x-1,x)|

    Text Solution

    |

  19. Evaluate the following determinants: |(1,0,0),(0,1,0),(0,0,1)|

    Text Solution

    |

  20. Evaluate the following determinants: |(1,-3,3),(4,-1,3),(3,5,3)|

    Text Solution

    |

  21. Evaluate the following determinants: |(1,0,2),(0,2,1),(2,0,3)|

    Text Solution

    |