Home
Class 12
MATHS
Prove that |{:(a^(2)+1,ab,ac),(ab,b^(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)`.

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    ARIHANT MATHS|Exercise Single Option Correct Type Questions|2 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise For Session 1|7 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

Similar Questions

Explore conceptually related problems

What is |{:(-a^(2),ab,ac),(ab,-b^(2),bc),(ac,bc,-c^(2)):}| equal to ?

Prove that : (i) |{:(a,c,a+c),(a+b,b,a),(b,b+c,c):}|=2 abc (ii) Prove that : |{:(a^(2),bc,ac+c^(2)),(a^(2)+ab,b^(2),ac),(ab,b^(2)+bc,c^(2)):}|=4a^(2)b^(2)c^(2)

What is the value of |(-a^(2),ab,ac),(ab,-b^(2),bc),(ac,bc,-c^(2))| ?

Prove that |{:(1, a, a^(2)-bc),(1, b, b^(2)-ca), (1, c, c^(2)-ab):}|=0

If A=[{:(0,c,-b),(-c,0,a),(b,-a,0):}] and B=[{:(a^(2),ab,ac),(ab,b^(2),bc),(ac,bc,c^(2)):}] , then (A+B)^(2)=

If D=|(a^(2)+1,ab,ac),(ba,b^(2)+1,bc),(ca,cb,c^(2)+1)| then D equal to

The determinant Delta=|{:(,a^(2)(1+x),ab,ac),(,ab,b^(2)(1+x),(bc)),(,ac,bc,c^(2)(1+x)):}| is divisible by

The determinant Delta = |(a^(2) + x^(2),ab,ac),(ab,b^(2) + x^(2),bc),(ac,bc,c^(2) + x^(2))| is divisible

ARIHANT MATHS-DETERMINANTS -Exercise (Questions Asked In Previous 13 Years Exam)
  1. Prove that |{:(a^(2)+1,ab,ac),(ab,b^(2)+1,bc),(ac,bc,c^(2)+1):}|=1+a...

    Text Solution

    |

  2. If a^(2)+b^(2)+c^(2)=-2 and f(x)= |{:(1+a^(2)x,(1+b^(2))x,(1+c^(2))x...

    Text Solution

    |

  3. The system of equations alphax+y+z=alpha-1, x+alphay+z=alpha-1 ...

    Text Solution

    |

  4. If a1,a2,a3,.....an.... are in G.P. then the determinant Delta=|[logan...

    Text Solution

    |

  5. If D =|{:(1,1,1),(1,1+x,1),(1,1,1+y):}|"for" " "xne0,yne0 then D is

    Text Solution

    |

  6. Consider the system of equations x-2y+3z=-1 -x+y-2z=k x-3y+4z=1 ...

    Text Solution

    |

  7. Let a,b,c, be any real number. Suppose that there are real numbers x,y...

    Text Solution

    |

  8. Let a,b,c be such that b(a+c)ne 0. If |{:(,a,a+1,a-1),(,-b,b+1,b-1),(,...

    Text Solution

    |

  9. If f(theta)=|{:(1,tantheta,1),(-tantheta,1,tantheta),(-1,-tantheta,1):...

    Text Solution

    |

  10. The number of values of k which the linear equations 4x+ky+2z=0 kx...

    Text Solution

    |

  11. If the trivial solution is the only solution of the system of equation...

    Text Solution

    |

  12. The number of values of k, for which the system of equations (k""+"...

    Text Solution

    |

  13. If alpha,beta!=0 , and f(n)""=alpha^n+beta^n and |3 1+f(1)1+f(2)1+f(1)...

    Text Solution

    |

  14. The set of the all values of lamda for which the system of linear equa...

    Text Solution

    |

  15. Which of the following values of alpha satisfying the equation |(1+alp...

    Text Solution

    |

  16. The system of linear equations x+lambday-z=0 lambdax-y-z=0 x+y-l...

    Text Solution

    |

  17. The total number of distinct x in R for which |[x, x^2, 1+x^3] , [2x,...

    Text Solution

    |

  18. Let a,lambda,mu in R, Consider the system of linear equations ax+2y=la...

    Text Solution

    |

  19. If S is the set of distinct values of ' b for which the following syst...

    Text Solution

    |