Home
Class 12
MATHS
Prove the following: [[a^2+1,ab,ac],[a...

Prove the following:
`[[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

  • CONTINUITY AND DIFFERENTIABILITY

    SHARAM PUBLICATION|Exercise EXAMPLE|156 Videos

  • DIFFERENTIAL EQUATION

    SHARAM PUBLICATION|Exercise EXAMPLE|124 Videos

Similar Questions

Explore conceptually related problems

Prove the following: [[-a^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=4a^2b^2c^2

Prove that [[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]] = 1+a^2+b^2+c^2 and hence show that its maximum value = 1

Prove that the following. [[b^2+c^2,ab,ac],[ab,c^2+a^2,bc],[ca,cb,a^2+b^2]]=4a^2b^2c^2

Prove the following: [[(b+c)^2,a^2,bc],[(c+a)^2,b^2,ca],[(a+b)^2,c^2,ab]] = (a^2+b^2+c^2)(a+b+c)(b-c)(c-a)(a-b)

Prove the following : [[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b)]] =0

Prove the following: [[b^2-ab,b-c,bc-ac],[ab-a^2,a-b,b^2-ab],[bc-ac,c-a,ab-a^2]]=0

If a, b and c are all positive real, then prove that minimum value of determinant |{:(a^2+1,ab,ac),(ab,b^2+1,bc),(ac,bc,c^2+1):}| = 1+a^2+b^2+c^2

Prove that the following. [[a,b,c],[a^2,b^2,c^2],[bc,ca,ab]] =(b-c)(c-a)(a-b)(bc+ca+ab)

show that |[a^2+x^2,ab ,ac],[ab,b^2+x^2,bc],[ac,bc,c^2+x^2]| is divisible x^4

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

SHARAM PUBLICATION-DETERMINANT-EXAMPLE
  1. Using properties of the determinants, prove that: |[2y, y-z-x, 2y],[2z...

    Text Solution

    |

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

    Text Solution

    |

  3. Show that: |[x, y ,z],[x^2, y^2, z^2], [yz, zx, xy ]|=(x-y)(y-z)(z-x)....

    Text Solution

    |

  4. Prove [[a^3-x^3,a^2,a],[b^3-x^3,b^2,b],[c^3-x^3,c^2,c]] = (a-b)(a-c)(b...

    Text Solution

    |

  5. Prove that: 1/(bc+ca+ab)|[a, b, c],[a^2, b^2, c^2], [bc, ca, ab]|=(b-c...

    Text Solution

    |

  6. Prove that: |[y+z, z, y],[z, z+x, x], [y, x, x+y]|= 4 xyz

    Text Solution

    |

  7. Prove that: |[a+3b, a+5b, a+7b],[a+4b, a+6b, a+8b], [a+5b, a+7b, a+9b]...

    Text Solution

    |

  8. Prove the following: [[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]] =1+...

    Text Solution

    |

  9. Prove the following: [[-a^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=4a^2b^...

    Text Solution

    |

  10. Prove the following: [[b^2-ab,b-c,bc-ac],[ab-a^2,a-b,b^2-ab],[bc-ac,...

    Text Solution

    |

  11. Show that: |[(y+z)^2, xy, zx],[xy, (x+z)^2, yz], [xz, yz, (x+y)^2]|=2x...

    Text Solution

    |

  12. If a, b, c, are in A.P. find the value of |[2y+4, 5y+7, 8y+a],[3y+5, 6...

    Text Solution

    |

  13. Prove the following: [[1,1,1],[a,b,c],[a^3,b^3,c^3]] =(b-c)(c-a)(a...

    Text Solution

    |

  14. If [[x,x^2,x^3-1],[y,y^2,y^3-1],[z,z^2,z^3-1]]=0 then prove that xyz...

    Text Solution

    |

  15. Prove the following: [[a+b+c,-c,-b],[-c,a+b+c,-a],[-b,-a,a+b+c]] =...

    Text Solution

    |

  16. Prove the following: [[b+c,a+b,a],[c+a,b+c,b],[a+b,c+a,c]] =a^3+b^...

    Text Solution

    |

  17. If ax+hy+g=0, hx+by+f=0 and gx+fy+c=lamda, find the value of lamda in ...

    Text Solution

    |

  18. Prove that abs((-2a,a+b,c+a),(a+b,-2b,b+c),(c+a,c+b,-2c))=4(b+c)(c+a)(...

    Text Solution

    |

  19. If 2s=a+b+c show that [[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[...

    Text Solution

    |

  20. If A+B+C = pi, prove that [[sin^2A,cotA,1],[sin^2B,cotB,1],[sin^2C,c...

    Text Solution

    |