Home
Class 12
MATHS
Prove that abs((-2a,a+b,c+a),(a+b,-2b,b+...

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

Promotional Banner

Topper's Solved these Questions

  • MATRICES DETERMINANTS PROBABILITY

    USHA PUBLICATION|Exercise EXERCISE|59 Videos

  • PRACTICE PAPER

    USHA PUBLICATION|Exercise PRACTICE PAPER|95 Videos

Similar Questions

Explore conceptually related problems

Prove that abs((a,b,c),(a^2,b^2,c^2),(bc,ca,ab))=(a-b)(b-c)(c-a)(ab+bc+ca)

Show that: abs((a,a^2,a^3),(b,b^2,b^3),(c,c^2,c^3))=abc(a-b)(b-c)(c-a)

Show that: abs((1,a,a^2),(1,b,b^2),(1,c,c^2))=(a-b)(b-c)(c-a)

Show that abs{:(b-c,c-a,a-b),(c-a,a-b,b-c),(a-b,b-c,c-a):}=0.

Prove that |(1, a, a^3),(1, b, b^3),(1, c, c^3)| = (a-b)(b-c)(c-a)(a+b+c).

USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Find the magnitude and equation of the line of shotest distance betwee...

    Text Solution

    |

  2. Solve the following by matrix method x-y+z=4, 2x+y-3z=0, x+y+z=2

    Text Solution

    |

  3. 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

    |

  4. Show that the function f : R^+toR^+ defined by f (x) =x+1/x is injecti...

    Text Solution

    |

  5. Solve "sin"^(-1)x-"cos"^(-1)x="cos"^(-1)sqrt(3)/(2)

    Text Solution

    |

  6. Solve: 2sin^(-1) x +sin^(-1) (1-x)= pi/2

    Text Solution

    |

  7. Evaluate intln(x^2+x+2)dx

    Text Solution

    |

  8. int0^pi((xtanx)/(secx+tanx))dx

    Text Solution

    |

  9. Solve the differential equation (dy)/(dx)= (y-x+1)/(y+x+5).

    Text Solution

    |

  10. Differentiate cos^(-1)(sinx) w.r.t.x.

    Text Solution

    |

  11. int(cot xdx)/(ln sin x) = ?

    Text Solution

    |

  12. How many independent constants are there in the general equation of a ...

    Text Solution

    |

  13. What is the range of the signum function?

    Text Solution

    |

  14. If the vectors hati+2hatj+hatk & 2hati+3hatj+alphahatk are perpendicul...

    Text Solution

    |

  15. Between tan 1 and tan^(-1)1, which is greater?

    Text Solution

    |

  16. Answer the following: In which inverval does the determinant A =[[1...

    Text Solution

    |

  17. What is AB – BA if A, B and AB are all symmetric matrices .

    Text Solution

    |

  18. If y =(cosx+sinx)/cosx, then what is dy/dx ?

    Text Solution

    |

  19. Write the order of the differential equation whose general solution is...

    Text Solution

    |

  20. Consider the binary operation * on the set {1,2,3,4,5} defined by a*...

    Text Solution

    |