Home
Class 12
MATHS
Let A=|1sintheta1-sintheta1sintheta-1-si...

Let `A=|1sintheta1-sintheta1sintheta-1-sintheta1|,` where `0lt=thetalt=2pidot` Then `D e t(A)=0` (b) `D e t(A) in (2,oo)` `D e t(A) in (2,4)` (d) `D e t(A) in [2,4]`

Text Solution

Verified by Experts

`Det (A) in[2,4]`

` [[1 , sin theta, 1], [-sin theta , 1 , sin theta ] ,[-1 , -sin theta , 1]]`

` [ [1 , sin theta , 2 ], [-sin theta , 1 , 0 ], [-1 ,-sin theta , 0]]` [using } `C_{3} arrow C_{3}+C_{1}] `

...
Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

  • DIFFERENTIABILITY

    RD SHARMA|Exercise Solved Examples And Exercises|136 Videos

Similar Questions

Explore conceptually related problems

Let A=[1sintheta1-sintheta1sintheta-1-sintheta1] , where 0lt=thetalt=2pi . Then (A) D e t(A)" "=" "0 (B) D e t(A) in (2,oo) (C) D e t(A) in (2," "4) (D) D e t(A) in [2," "4]

If cos^2theta-sintheta=1/4 then sintheta=?

Let A=[(1,sintheta, 1),(-sintheta, 1, sintheta),(-1, -sintheta, 1)], where 0lethetalt2pi then (A) |A|=0 (B) |A|epsilon[2,4] (C) |A|epsilon)(0,oo) (D) |A|epsilon(2,oo)

If Delta=|{:(1,sintheta,1),(-sintheta,1,sintheta),(-1,-sintheta,1):}|"prove that" 2lt=Deltalt=4.

inte^(sintheta)[log(sintheta)+cosec^(2)theta]costheta"d"theta=

Prove that int_0^(pi/2)(costheta-sintheta)/(1+sintheta.costheta)d theta=0.

If A = [(1,sintheta,1),(-sintheta,1,sintheta),(-1,-sintheta,1)] , then for all thetain ((3pi)/(4),(5pi)/(4)) , det. (A) lies in the interval

" 7."int(sintheta)/((1+cos theta)^(2))d theta

If {:A=[(costheta,-sintheta),(sintheta,costheta)]:},"then" A^T+A=I_2 , if

RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. L e t|3y x1|=|3 2 4 1| . Find possible values of xa n dy are natural n...

    Text Solution

    |

  2. If |[x-2,-3],[3x,2x]|=3 find the value of x

    Text Solution

    |

  3. Let A=|1sintheta1-sintheta1sintheta-1-sintheta1|, where 0lt=thetalt=2p...

    Text Solution

    |

  4. Find the minors of cofactors of elements of the matrix A=[a(i j)]=[[1,...

    Text Solution

    |

  5. Evaluate =|[-1, 6,-2],[ 2, 1, 1],[ 4, 1,-3]| by two methods

    Text Solution

    |

  6. If A=[1 3 2 1] , find the determinant of the matrix A^2-2Adot

    Text Solution

    |

  7. Determine the values of x for which the matrix A=[x+1-3 4-5x+2 2 4 1x-...

    Text Solution

    |

  8. The value of the determinant |xx+y x+2y x+2y xx+y x+y x+2y x|i s 9x^2...

    Text Solution

    |

  9. Let f(x)=|[cosx , x , x] , [2sinx , x , 2x] , [sinx , x , x]|, then ...

    Text Solution

    |

  10. A triangle has its three sides equal to a , b and c . If the coordin...

    Text Solution

    |

  11. Solve the following system of equations using Cramers rule. 5x-7y+z=1...

    Text Solution

    |

  12. Let A=|1sintheta1-sintheta1sintheta-1-sintheta1|, where 0lt=thetalt=2p...

    Text Solution

    |

  13. Prove the identities: |[a, b-c,c-b],[ a-c, b, c-a],[ a-b,b-a, c]| =(...

    Text Solution

    |

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

    Text Solution

    |

  15. |((a^2+b^2)/c,c,c),(a,(b^2+c^2)/a,a),(b,b,(a^2+c^2)/b)| equal to : (A)...

    Text Solution

    |

  16. Prove that identities: |[-bc,b^2+bc,c^2+bc],[a^2+ac,-ac,c^2+ac],[a^2+...

    Text Solution

    |

  17. Without expanding, prove that |a b c x y z p q r|=|x y z p q r a b c|=...

    Text Solution

    |

  18. If |[p, b, c],[ a, q, c],[ a, b, r]|=0, find the value of p/(p-a)+q/(...

    Text Solution

    |

  19. Find the equation of the line joining A(1,3)a n dB(0,0) using determin...

    Text Solution

    |

  20. If A(x1, y1),B(x2, y2) and C(x3,y3) are vertices of an equilateral ...

    Text Solution

    |