Home
Class 12
MATHS
Show without expanding at any stage that...

Show without expanding at any stage that: ` [0,sinalpha-cosalpha],[-sinalpha,0,sinbeta],[cosalphas-sinbeta,0]|=0 `

Text Solution

Verified by Experts

The correct Answer is:
`0`
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Exercise 4(b) (LONG ANSWER TYPE QUESTIONS (II))|48 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Exercise 4(c ) (SHORT ANSWER TYPE QUESTIONS)|4 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Exercise 4(b) (SHORT ANSWER TYPE QUESTIONS)|11 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

  • DIFFERENTIAL EQUATIONS

    MODERN PUBLICATION|Exercise CHAPTER TEST (9)|12 Videos

Similar Questions

Explore conceptually related problems

Evaluate : Delta=|{:(0,sinalpha,-cosalpha),(-sinalpha,0,sinbeta),(cosalpha,-sinbeta,0):}| .

Show without expanding at any stage that: | (1,cosalpha-sinalpha, cosalpha+sinalpha),(1,cosbeta-sinbeta,cosbeta+sinbeta),(1, cosgamma-singamma,cosgamma+singamma)| =2 |(1,cosalpha, sinalpha),(1,cosbeta, sinbeta),(1,cosgamma,singamma)|

Show without expanding at any stage that: [0,a,-b],[-a,0,-c],[b,c,0]|=0

If A_(alpha)=[(cosalpha,-sinalpha),(sinalpha,cosalpha)] , then

costheta-sintheta=cosalpha-sinalpha

If cosalpha+cosbeta=0=sinalpha+sinbeta , then cos2alpha+cos2beta=?

Show by vector method that sin(alpha-beta)=sinalphacosbeta-cosalpha sinbeta.

Evaluate the following: |[cosalpha, sinalpha],[sinalpha, cosalpha]|

If A=[(0,sin alpha, sinalpha sinbeta),(-sinalpha, 0, cosalpha cosbeta),(-sinalpha sinbeta, -cosalphacosbeta, 0)] then (A) |A| is independent of alpha and beta (B) A^-1 depends only on beta (C) A^-1 does not exist (D) none of these

Let A_(alpha)=[(cosalpha, -sinalpha,0),(sinalpha, cosalpha, 0),(0,0,1)] , then :

MODERN PUBLICATION-DETERMINANTS-Exercise 4(b) (LONG ANSWER TYPE QUESTIONS (I))
  1. Using the property of determinants and without expanding, prove that |...

    Text Solution

    |

  2. Without actual expansion, prove that the following determinants vanish...

    Text Solution

    |

  3. Using the property of determinants and without expanding in questions ...

    Text Solution

    |

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

    Text Solution

    |

  5. witout expanding at any stage Prove that |{:(0,,a,,-b),(-a,,0,,-...

    Text Solution

    |

  6. Without actual expansion, prove that the following determinants vanish...

    Text Solution

    |

  7. The value of the determinant |{:(1,bc,a(b+c)),(1,ca,b(a+c)),(1, ab,c(a...

    Text Solution

    |

  8. Without expanding the determinants show that : ((1)/(a)+(1)/(b)+(1)/...

    Text Solution

    |

  9. Prove that : |{:(x-y-z,2x,2x),(2y,y-z-x,2y),(2z,2z,z-x-y):}|

    Text Solution

    |

  10. Without expanding the determinant, prove that |a a^2b c bb^2c a cc^2a ...

    Text Solution

    |

  11. Show without expanding at any stage that: [0,sinalpha-cosalpha],[-sin...

    Text Solution

    |

  12. " If " |{:(x^(2)+x,,x+1,,x-2),(2x^(2)+3x-1,,3x,,3x-3),(x^(2)+2x+3,,2x...

    Text Solution

    |

  13. Evaluate the following : |{:(b+c,a,a),(b,c+a,b),(c,c,a+b):}|

    Text Solution

    |

  14. Evaluate the following : |{:(x+lambda,x,x),(x,x+lambda,x),(x,x,x+lam...

    Text Solution

    |

  15. Evaluate the following: |[1, a, b+c],[1, b, c+a],[1, c, a+b]|

    Text Solution

    |

  16. Evaluate: [[x,y,x+y],[y,x+y,x],[x+y,x,y]]

    Text Solution

    |

  17. Evaluate the following: |[1,x,y],[1, x+y, y],[1, x, x+y]|

    Text Solution

    |

  18. Prove that: |[b+c, c=a, a+b],[q+r, r+p, p+q],[y+z, z+x, x+y]|=2|[a,b,...

    Text Solution

    |

  19. Use the properties of determinant and without expanding prove that |...

    Text Solution

    |