Home
Class 12
MATHS
Matrix=[[e^t,e^-t(sint-2cost),e^-t(-2sin...

Matrix`=[[e^t,e^-t(sint-2cost),e^-t(-2sint-cost)],[e^t,-e^-t(2sint+cost),e^-t(sint-2cost)],[e^t,e^tcost,e^-tsint]]` is invertible. (a) only if `t=(pi)/(2)` (b) only `y=pi` (c) `tepsilonR` (d) `t!inR`

A

invertible only if `t = (pi)/(2)`

B

not invertible for any `t in R`

C

invertible for all `t in R`

D

invertible only if `t = pi`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Ifint_(pi/3)^xsqrt((3-sin^2t))dt+int_0^ycostdt=0,t h e ne v a l u a t e(dy)/(dx)

Let U(x,y,z) = xyz, x=e^(-t), y=e^(-t) cos t, z= sin t, t in R . Find (dU)/(dt) .

For the curve x = e^(t) cos t, y = e^(t) sin t the tangent line is parallel to x-axis when t is equal to

Ifg(x)=int_0^x(|sint|+|cost|)dt ,t h e ng(x+(pin)/2) is equal to, where n in N , g(x)+g(pi) (b) g(x)+g((npi)/(n2)) g(x)+g(pi/2) (d) none of these

If int_(0)^(x)f(t)dt=e^(x)-ae^(2x)int_(0)^(1)f(t)e^(-t)dt , then

x=tcost ,y=t+sintdot Then (d^(2x))/(dy^2)at t=pi/2 is (a)(pi+4)/2 (b) -(pi+4)/2 (c) -2 (d) none of these

Prove that the curve represented by x=3(cost+sint),y=4(cost-sint),t in R , is an ellipse

If w=x+2y+z^(2) and x=cost,y =sint,z =t . Find (dw)/(dt) .

Prove that int_0^x e^(x t)e^-t^2dt=e^(x^(2)/4)int_0^x e^-(t^(2)/4)dt

CENGAGE-JEE 2019-MCQ
  1. If the system of linear equations x-4y+7z=g, 3y-5z=h, -2x+5y-9z=k is c...

    Text Solution

    |

  2. If the system fo equations x+y+z = 5 x + 2y + 3z = 9 x + 3y + a...

    Text Solution

    |

  3. Let a(1),a(2),a(3), …, a(10) be in G.P. with a(i) gt 0 for i=1, 2, …, ...

    Text Solution

    |

  4. If the system of linear equations 2x+2y+3z=a 3x-y+5z=b x-3y+2z=...

    Text Solution

    |

  5. prove that [ [a-b-c , 2a , 2a ] , [2b , b-c-a , 2b ] ,[2c ,2c,c-a-b]]=...

    Text Solution

    |

  6. An ordered pair (alpha, beta) for which the system of linear equations...

    Text Solution

    |

  7. The set of all values of lambda for which the system of linear equatio...

    Text Solution

    |

  8. If A = [(costheta,-sintheta),(sintheta,costheta)], then the matrix A^(...

    Text Solution

    |

  9. Matrix=[[e^t,e^-t(sint-2cost),e^-t(-2sint-cost)],[e^t,-e^-t(2sint+cost...

    Text Solution

    |

  10. Let d in R and A= ((-2,4+d, sintheta-2),(1, sintheta+2,d),(5, 2sinthet...

    Text Solution

    |

  11. Let A=[(2,b,1),(b,b^(2)+1,b),(1,b,2)] where b gt 0. Then the minimum v...

    Text Solution

    |

  12. Let A=[[0,2q,r] , [p,q,-r] , [p,-q,r]] If A A^T=I3 then |p|=

    Text Solution

    |

  13. Let A and B be two invertible matrices of order 3xx3. If det. (ABA^(T)...

    Text Solution

    |

  14. Let P=[(1,0,0),(4,1,0),(16,4,1)] and I be the identity matrix of order...

    Text Solution

    |

  15. If A = [(1,sintheta,1),(-sintheta,1,sintheta),(-1,-sintheta,1)], then ...

    Text Solution

    |

  16. Two cards are drawn successively with replacement from a well-shuffled...

    Text Solution

    |

  17. An urn contains 5 red and 2 green balls. A ball is drawn at random fro...

    Text Solution

    |

  18. An unbiased coin is tossed. If the result is a head, a pair of unbi...

    Text Solution

    |

  19. If the probability of hitting a target by a shooter, in any shot is 1/...

    Text Solution

    |

  20. In a random experiment, a fair die is rolled until two fours are obtai...

    Text Solution

    |