Home
Class 12
MATHS
Prove that,abs((-a^2,ab,ac),(ba,-b^2,bc)...

Prove that,`abs((-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2))`=4`a^2b^2c^2`.

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

Prove that, abs((a^2+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1)) =1+ a^2+b^2+c^2 .

|{:(a^2,ab,ac),(ab,b^2,bc),(ca,bc,c^2):}|= ?

Using the property of determinants and without expanding {:|( -a^(2) , ab,ac),( ba,-b^(2) , bc) ,( ca, cb, -c^(2)) |:} =4a^(2) b^(2) c^(2)

Show that |{:(a^(2)+1,ab,ac),(ab,b^(2)+1,bc),(ca,bc,c^(2)+1):}|=1+a^(2)+b^(2)+c^(2)

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

Evalute |{:(0,c,b),(c,0,a),(b,a,0):}| and hence show that, |{:(" "-a^2," "ab," "ac),(" "ab," "-b^2," "bc),(" "ca," "bc," "-c^2):}|=4a^2b^2c^2

prove that , |{:(a,a^2,a^3+bc),(b,b^2,b^3+ca),(c,c^2,c^3+ab):}|=(a-b)(b-c)(c-a)(abc+bc+ca+ab)

Show that, |{:(a^2+10,ab,ac),(ab,b^2+10,bc),(ca,bc,c^2+10):}| is divisible by 100 .

|{:(0,ab^2,ac^2),(a^2b,0,bc^2),(a^2c,cb^2,0):}|=2a^3b^3c^3

Prove the identities: |[b^2+c^2,ab, ac],[ba,c^2+a^2,bc],[ca, cb ,a^2+b^2]|=4a^2b^2c^2

CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. If ar=(cos2rpi+i sin 2rpi)^(19) , then prove that |[a1,a2,a3],[a4,a5,a...

    Text Solution

    |

  2. Let f(x)=|(2cos^2x,sin2x,-sinx),(sin2x,2sin^2x,cosx),(sinx,-cosx,0)| ....

    Text Solution

    |

  3. Prove that,abs((-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2))=4a^2b^2c^2.

    Text Solution

    |

  4. The number of positive integral solutions of the equation |(x^3+1,x^2y...

    Text Solution

    |

  5. If the value of the determinant |(a,1, 1) (1,b,1) (1,1,c)| is positive...

    Text Solution

    |

  6. By using properties of determinants. Show that: (i) |(x+4,2x,2x),(2x,...

    Text Solution

    |

  7. Using properties of determinants, evaluate |[18, 40 ,89],[ 40 ,89, 198...

    Text Solution

    |

  8. If A1,B1,C1, are respectively, the cofactors of the elements a1, b1,c...

    Text Solution

    |

  9. Solve for x |x-2 2x-3 3x-4 x-4 2x-9 3x-16 x-8 2x-27 3x-64|...

    Text Solution

    |

  10. If Delta1=|[x, b, b],[ a, x, b],[ a, a, x]| a n d Delta2=|[x, b],[ a, ...

    Text Solution

    |

  11. Without expanding evaluate the determinant |[sinalpha,cosalpha,sin(alp...

    Text Solution

    |

  12. If y= sin px and y(n) is the nth derivative of y, then |{:(y,y(1),y(...

    Text Solution

    |

  13. Find the value of the determinant |[1, 1, 1, 1],[ 1, 2, 3, 4],[ 1, 3, ...

    Text Solution

    |

  14. The parameter on which the value of the determinant |1 a...

    Text Solution

    |

  15. If x=c y+b z ,y=a z+c x ,z=bx+a y ,w h e r e .x ,y ,z are not all ze...

    Text Solution

    |

  16. If |[b^2+c^2,a b,a c],[ a b, c^2+a^2,b c],[c a, c b, a^2+b^2]|=k a^2b^...

    Text Solution

    |

  17. The value of |[-1, 2, 1],[ 3+2sqrt(2), 2+2sqrt(2), 1],[ 3...

    Text Solution

    |

  18. Find the following system of equations is consistent, (a+1)^3x+(a+2)...

    Text Solution

    |

  19. Prove the identities: |[b^2+c^2,ab, ac],[ba,c^2+a^2,bc],[ca, cb ,a^2+...

    Text Solution

    |

  20. If |[1 1 1];[a b c];[ a^3b^3c^3]|=(a-b)(b-c)(c-a)(a+b+c),w h e r ea ,b...

    Text Solution

    |