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

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

Text Solution

Verified by Experts

The correct Answer is:
`4a^2b^2c^2`
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise Practice Work|90 Videos

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise Textbook based MCQs|42 Videos

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise Exercise 4.6|16 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    KUMAR PRAKASHAN|Exercise Practice Paper - 5 (Section-D)|4 Videos

  • INTEGRALS

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER-7 (SECTION-D)|2 Videos

Similar Questions

Explore conceptually related problems

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2):}|=4a^2b^2c^2

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(a^2+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1):}|=1+a^2+b^2+c^2

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):}|

Prove that |{:(a,a+b,a=b+c),(2a,3a+2b,4a+3b+2c),(3a,6a+3b,10a+6b+3c):}|=a^3

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)) ]:}

The determinant |{:(b^2-ab,b-c,bc-ac),(ab-a^2,a-b,b^2-ab),(bc-ac,c-a,ab-a^2):}| equals …….

Using the properties of determinants, prove the following |{:(a^2,b^2,c^2),((a+1)^2,(b+1)^2,(c+1)^2),((a-1)^2,(a-1)^2,(c-1)^2):}|=4|{:(a^2,b^2,c^2),(a,b,c),(1,1,1):}|

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

If Deltan=|{:(a^(2)+n,ab,ac),(ab,b^(2)+n,bc),(ac,bc,c^(2)+n):}|,n in N and the equation x^(3)-lambdax^(2)+11x-6=0 has roots a,b,c and a,b,c are in AP. The value of (Delta2_(n))/(Delta_(n)) is

KUMAR PRAKASHAN-DETERMINANTS -MISCELLANEOUS EXERCISE - 4
  1. Prove that the determinent |{:(x,sintheta,costheta),(-sintheta,-x,1),(...

    Text Solution

    |

  2. Without expanding the determinant prove that |{:(a,a^2,bc),(b,b^2,ca),...

    Text Solution

    |

  3. Evaluate |{:(cosalphacosbeta,cosalphasinbeta,-sinalpha),(-sinbeta,cosb...

    Text Solution

    |

  4. If a, b and c are real numbers , and Delta=|{:(b+c,c+a,a+b),(c+a,a+b,b...

    Text Solution

    |

  5. Solve the equation |{:(x+a,x,x),(x,x+a,x),(x,x,x+a):}|=0. (ane0)

    Text Solution

    |

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

    Text Solution

    |

  7. If A^(-1)=[{:(3,-1,1),(-15,6,-5),(5,-2,2):}] and B=[{:(1,2,-2),(-1,3,0...

    Text Solution

    |

  8. Let A=[{:(1,-2,1),(-2,3,1),(1,1,5):}] Verify that [adjA]^(-1)=adj(A^...

    Text Solution

    |

  9. Let A=[{:(1,-2,1),(-2,3,1),(1,1,5):}] Verify that (A^(-1))^-1=A

    Text Solution

    |

  10. Evaluate |{:(x,y,x+y),(y,x+y,x),(x+y,x,y):}|

    Text Solution

    |

  11. Evaluate |{:(1,x,y),(1,x+y,y),(1,x,x+y):}|

    Text Solution

    |

  12. Using properties of determinants in Exercise 11 to 15 prove that |{:...

    Text Solution

    |

  13. Using properties of determinants in Exercise 11 to 15 prove that |{:...

    Text Solution

    |

  14. Using properties of determinants in Exercise 11 to 15 prove that |{:...

    Text Solution

    |

  15. Using properties of determinants in Exercise 11 to 15 prove that |{:...

    Text Solution

    |

  16. Using properties of determinants in Exercise 11 to 15 prove that |{:...

    Text Solution

    |

  17. Solve the following system of linear equations 2/x+3/y+(10)/z=4 4/...

    Text Solution

    |

  18. If a,b,c are in A.P then the determinant |{:(x+2,x+3,x+2a),(x+3,x+4,...

    Text Solution

    |

  19. If x,y,z are nonzero real numbers, then the inverse of matrix A=[{:(x,...

    Text Solution

    |

  20. Let A=[{:(1,sintheta,1),(-sintheta,1,sintheta),(-1,-sintheta,1):}] w...

    Text Solution

    |