Home
Class 12
MATHS
If A=[(cosalpha,-sinalpha),(sinalpha,cos...

If `A=[(cosalpha,-sinalpha),(sinalpha,cosalpha)]` is identity matrix, then write the value of `alpha` .

Text Solution

Verified by Experts

Given that,
`A=[(cosalpha,-sinalpha),(sinalpha,cosalpha)]=I`
`[(cosalpha,-sinalpha),(sinalpha,cosalpha)]=[[1,0],[0,1]]`
Equating both sides,
`cos alpha =1`
`alpha =0`

To verify,
...
Promotional Banner

Topper's Solved these Questions

  • ADJOINTS AND INVERSE OF MATRIX

    RD SHARMA|Exercise QUESTION|1 Videos

  • ALGEBRA OF VECTORS

    RD SHARMA|Exercise Solved Examples And Exercises|331 Videos

Similar Questions

Explore conceptually related problems

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

If A=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}] , show that A'A=I.

If A=[{:(cosalpha,-sinalpha),(sinalpha,cosalpha):}] , then find the least value of alpha for which A+A'=I.

If A=[[cosalpha, sinalpha], [-sinalpha, cosalpha]] , then A^(10)=

If A_(alpha)=[(cosalpha,sinalpha),(-sinalpha,cosalpha)] then (A_(alpha))^2=?

if A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] be such that A+A'=I then alpha

RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. If [(a+b,2),( 5,b)]=[(6, 5),( 2, 2)] , then find adot

    Text Solution

    |

  2. If A is a matrix of order 3xx4 and B is a matrix of order 4xx3 , find ...

    Text Solution

    |

  3. If A=[(cosalpha,-sinalpha),(sinalpha,cosalpha)] is identity matrix, t...

    Text Solution

    |

  4. If [(1, 2),( 3, 4)][(3, 1),( 2, 5)]=[(7, 11),( 23, k)] , then write t...

    Text Solution

    |

  5. If I is the identity matrix and A is a square matrix such that A...

    Text Solution

    |

  6. If A=[(1, 2),( 0, 3)] is written as B+C , where B is a symmetric matri...

    Text Solution

    |

  7. If A is 2 times 3 matrix and B is a matrix such that A^T\ B and B A^T ...

    Text Solution

    |

  8. What is the total number of 2xx2 matrices with each entry 0 or 1...

    Text Solution

    |

  9. If [[x,x-y],[2x+y,7]]=[[3 ,1],[ 8, 7]] , then find the value of y

    Text Solution

    |

  10. If a matrix has 5 elements, write all possible orders it can have.

    Text Solution

    |

  11. For a 2xx2 matrix A=[a(i j)] whose elements are given by a(i j)=i/j...

    Text Solution

    |

  12. If x [[2 ],[3]]+y[[-1],[ 1]]=[[10],[ 5]] , find the value of x

    Text Solution

    |

  13. If [[9,-1, 4],[-2, 1, 3]]=A+[[1 ,2,-1],[ 0, 4, 9]] , then find matrix ...

    Text Solution

    |

  14. If [(a-b,2a+c),(2a-b,3c+d)]=[(-1, 5),( 0, 13)] , find the value of b

    Text Solution

    |

  15. For what value of x is the matrix A=[(0,1,-2),(1,0,3),(x,3,0)] a skew-...

    Text Solution

    |

  16. If matrix A=[[2,-2],[-2, 2]] and A^2=p A , then write the value of p

    Text Solution

    |

  17. If A is a square matrix such that A^2=A , then write the value of 7A-(...

    Text Solution

    |

  18. If 2[[3, 4, 5x]]+[[1y,0, 1]]=[[7 0, 10, 5]] , find x-y .

    Text Solution

    |

  19. If [[x,1]][(1 ,0),(-2, 0)]=O , find x

    Text Solution

    |

  20. If [a+4 3b8-6]=[2a+2b+2 8a-8b] , write the value of a-2b .

    Text Solution

    |