Home
Class 12
MATHS
By using the properties of determinants,...

By using the properties of determinants,prove that
`|[a^2+1,ab ,ac],[ab,b^2+1,bc],[ca ,cb,c^2+1]|=1+a^2+b^2+c^2`

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    V PUBLICATION|Exercise QUESTION BANK|168 Videos

  • DIFFERENTIAL EQUATIONS

    V PUBLICATION|Exercise QUESTION BANK|149 Videos

Similar Questions

Explore conceptually related problems

By using properties of determinants, prove that |[-a^2,ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]|=4a^2b^2c^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

By using the properties of determinants,prove that |[1+a^2-b^2,2ab ,-2b],[2ab,1-a^2+b^2,2a],[2b ,-2a,1-a^2-b^2]|=(1+a^2+b^2)^3

using properties of determinants, prove that abs[[1,a,a^2],[1,b,b^2],[1,c,c^2]]=(a-b)(b-c)(c-a) .

Show that Delta=abs[[-a^2,ab,ac],[ba,-b^2,bc],[ac,bc,-c^2]]=4a^2b^2c^2

Using properties of determinants, prove that |[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]| = 3(a+b+c)(ab+bc+ca)

Using properties of determinants prove the following. abs[[b+c,a,a],[b,c+a,b],[c,c,a+b]]=4abc

Using properties of determinants, show that abs[[a,a^2,b+c],[b,b^2,c+a],[c,c^2,a+b]]=(b-c)(c-a)(a-b)(a+b+c)

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 properties of determinants prove the following. abs[[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

V PUBLICATION-DETERMINANT-QUESTION BANK
  1. Using properties of determinants prove the following. abs[[1,x,x^2...

    Text Solution

    |

  2. Prove |[1+a^2-b^2, 2 a b, -2 b],[ 2 a b, 1-a^2+b^2, 2 a],[ 2 b,...

    Text Solution

    |

  3. By using the properties of determinants,prove that |[a^2+1,ab ,ac],[a...

    Text Solution

    |

  4. Let A be a square matrix of order 2x2 thenabs[KA] is equal to

    Text Solution

    |

  5. Which of the following is correct? a)Determinant is a square matrix ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. Find the area of the triangle with vertices at (1,0),(6,0),(4,3) using...

    Text Solution

    |

  9. Using the property of determinants,show that the points A(a,b+c),B(b...

    Text Solution

    |

  10. Find the values of k if area of triangle is 4 sq. units and vertices a...

    Text Solution

    |

  11. Find the equation of line joining (1,2) and (3,6) using determinants.

    Text Solution

    |

  12. If area of triangle is 35 sq. units with vertices (2,-6), (5,4) and (k...

    Text Solution

    |

  13. Find the minor of 1 in the determinant Delta=|[3, 4, 5 ],[2, 7, 1]...

    Text Solution

    |

  14. Find minors of element 6 in the determinant Delta=|[ 1, 2, 3],[ 4, ...

    Text Solution

    |

  15. Find minors and cofactors of the elements of the determinant |[1 , -2]...

    Text Solution

    |

  16. Find minors and cofactors of the elements a(11), a(21) in the determin...

    Text Solution

    |

  17. Find minors and cofactors of the elements of the determinant |[2, -3,...

    Text Solution

    |

  18. Write Minors and Cofactors of the elements of following determinants: ...

    Text Solution

    |

  19. Using cofactors of element of second row evaluate Delta=|[5, 3, 8],[...

    Text Solution

    |

  20. Using co-factors of elements of third column, evaluate Delta=|[1, x,...

    Text Solution

    |