Home
Class 12
MATHS
If A=[[alpha ,beta],[ gamma , -alpha]]...

If `A=[[alpha ,beta],[ gamma , -alpha]]` is such that `A^2=I`, then A) `1+alpha^2+beta gamma=0` B) `1-alpha^2+beta gamma=0` C)`1-alpha^2-beta gamma=0^`D)`1+alpha^2-beta gamma=0`

A

`1+alpha^2+beta gamma=0`

B

'1-alpha^2+beta y=0'

C

'1-alpha^2-beta gamma=0^'

D

'1+alpha^2-beta gamma=0'

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • LINEAR PROGRAMMING

    V PUBLICATION|Exercise QUESTION BANK|39 Videos

  • PROBABILITY

    V PUBLICATION|Exercise QUESTION BANK|132 Videos

Similar Questions

Explore conceptually related problems

If a, b and c are in geometric progression and the roots of the equations ax^(2)+2bx+c=0 are alpha and beta and those cx^(2)+2bx+a=0 are gamma and delta , then : a) alpha ne beta ne gamma ne delta b) alpha ne beta and gamma ne delta c) alpha=abeta=cgamma=cdelta d) alpha=beta and gamma ne delta

Let A=[(0,2beta,gamma),(alpha,beta,-gamma),(alpha,-beta,gamma)] be 3xx3 matrix Find A^T

If alpha, beta, gamma are the roots of the equation x^(3)+4x+1=0 , then find the value of (alpha+beta)^(-1) +(beta +gamma)^(-1) + (gamma+ alpha)^(-1)

Let A=[(0,2beta,gamma),(alpha,beta,-gamma),(alpha,-beta,gamma)] be 3xx3 matrix If A^T.A=6I, then alpha,beta and gamma is -

If cos alpha + 2cos beta+ 3 cos gamma = 0, sin alpha + 2sin beta +3 sin gamma= 0 and alpha + beta + gamma= pi , then sin 3alpha + 8 sin 3 beta + 27 sin 3 gamma =

If alpha+beta =pi//2andbeta+gamma=alpha , then tanalpha equals

If A(alpha, beta) = [(cos alpha, sin alpha, 0),(- sin alpha, cos alpha, 0),(0,0,e^beta)] then A(alpha, beta)^(-1) is equal to a) A(-alpha, -beta) b) A(-alpha,beta) c) A(alpha, - beta) d) A(alpha, beta)

V PUBLICATION-MATRICES-QUESTION BANK
  1. Find the values of x, y, z, if the matrix A=[[0, 2 y, z],[ x, y, ...

    Text Solution

    |

  2. For what values of x:[[1, 2, 1]] [[1, 2, 0],[ 2, 0, 1],[ 1, 0...

    Text Solution

    |

  3. If A=[[3,1],[-1,2]] then Hence show that A^2-5A+7I=0

    Text Solution

    |

  4. Find x, if [[x,-5,-1]] [[1, 0, 2],[ 0, 2, 1],[ 2, 0, 3]][[x],[...

    Text Solution

    |

  5. Find the matrix X so that X[[1 , 2, 3],[ 4, 5, 6]]=[[-7, -8, -9]...

    Text Solution

    |

  6. If A and B are square matrices of the same order such that A B=B A,the...

    Text Solution

    |

  7. If A=[[alpha ,beta],[ gamma , -alpha]] is such that A^2=I, then A) ...

    Text Solution

    |

  8. If the matrix A is both symmetric and skew symmetric, then: A)A is a d...

    Text Solution

    |

  9. If A is a square matrix such that A^2=A, then (I+A)^3-7 A is equal to ...

    Text Solution

    |

  10. Construct a m xx n matrix A=[[a(ij)]] whose elements a(ij) is given by...

    Text Solution

    |

  11. If [[a+b ,2],[ 5 , a b]]=[[6 , 2],[ 5, 8]], find the values of a an...

    Text Solution

    |

  12. Complete the following product [[1 , 0 , -5],[ 2, 0, 4]][[3 , 1],[ ...

    Text Solution

    |

  13. Find the product [[2],[ -1],[ 3]][[1 , 3 ,6]]

    Text Solution

    |

  14. If omega is a complex cube root of unity, show that [[1 , omega, ome...

    Text Solution

    |

  15. If A(alpha)=[[cos alpha, sin alpha],[ -sin alpha , cos alpha]], then...

    Text Solution

    |

  16. Show that the matrix A=[[1 ,-1, 1],[ 1, -1, 1],[ 1, -1, 1]] is...

    Text Solution

    |

  17. There are three families. Family A consists of 2 men, 3 women and 1 ch...

    Text Solution

    |

  18. Express [[4 , 3 , 7],[ 6 , 5, -8],[ 1, 2, 6]] as the sum of a sy...

    Text Solution

    |

  19. a) Construct a 3 xx 3 matrix A whose elements are given by a(ij)=2 i-j...

    Text Solution

    |

  20. A=[[1, 4, -1],[ 2, 5, 4],[ -1, -6, 3]]Write A as the sum of a ...

    Text Solution

    |