Home
Class 12
MATHS
If A=[[0, -tan (alpha/2)], [ tan (alpha...

If `A=[[0, -tan (alpha/2)], [ tan (alpha/2), 0]]` and `I` is the identity matrix of order 2 , show that `I+A=(I-A)[[cos alpha, -sin alpha],[ sin alpha, cos alpha]]`

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

Find inverse of the matrix A=[[cos alpha, -sin alpha, 0 ],[ sin alpha, cos alpha, 0],[ 0, 0, 1]]

Find the inverse of each of the matrices. [[1, 0, 0],[ 0 , cos alpha, sin alpha],[ 0, sin alpha, -cos alpha]]

If A = [(cos alpha,sin alpha),(-sin alpha,cos alpha)] then A^(10) is equal to

If A=[[cos alpha, -sin alpha],[sin alpha, cos alpha]] , then A+A^T=I if the value of alpha is

if A=[[sin alpha, cos alpha],[-cos alpha, sin alpha]] , then verify A^T A=I

If A_(alpha)=[[cos alpha, sin alpha],[ -sin alpha , cos alpha]] , then prove that i) A_(alpha ). A_(beta)=A_(alpha + beta) ii) (A_alpha)^n=[[cos n alpha, sin n alpha],[ -sin n alpha, cos n alpha]] for every positive integer n .

If cos alpha + sin alpha = (3)/(4) , then sin^(6) alpha + cos^(6) alpha is equal to

Evaluate Delta=|[0, sin alpha, -cos alpha],[ -sin alpha, 0 , sin beta],[ cos alpha, -sin beta, 0]|

Find the modulus of the following complex numbers i) 1+i tan alpha ii) tan alpha-i iii) 1-sin alpha+i cos alpha

V PUBLICATION-MATRICES-QUESTION BANK
  1. If A=[[1, 0, 2],[ 0, 2, 1],[ 2, 0, 3]], prove that A^3-6 A^2+7...

    Text Solution

    |

  2. If A=[[3,-2],[4,-2]] and I=[[1,0],[0,1]], find k so that A^2=kA-2I

    Text Solution

    |

  3. If A=[[0, -tan (alpha/2)], [ tan (alpha/2), 0]] and I is the identi...

    Text Solution

    |

  4. A trust fund has Rs. 30,000 that must be invested in two different typ...

    Text Solution

    |

  5. The bookshop of a particular school has 10 dozen chemistry books, 8 do...

    Text Solution

    |

  6. Assume that X,Y,Z,W and P are matrices of order 2xxn, 3xxk, 2xxp, nx...

    Text Solution

    |

  7. Assume that X,Y,Z,W and P are matrices of order 2xxn, 3xxk, 2xxp, nxx...

    Text Solution

    |

  8. If A=[[3 ,sqrt3, 2],[ 4 , 2, 0]] and B=[[2 , (-1), 2],[ 1, 2, 4...

    Text Solution

    |

  9. If A=[[-2],[4],[5]] B=[[1,3,6]] (AB)^T=B^TA^T

    Text Solution

    |

  10. For any square matrix A with real number entries.Prove that A+A^' is a...

    Text Solution

    |

  11. Prove that any square matrix can be expressed as the sum of a symmetic...

    Text Solution

    |

  12. Express the matrix [[2,-2,-4],[-1,3,4],[1,-2,-3]] as the sum of a ...

    Text Solution

    |

  13. Find the transpose of each of the following matrices: (i) [[5], [1/2]...

    Text Solution

    |

  14. If A=[[-1, 2, 3],[ 5, 7, 9],[ -2, 1 , 1]] and B=[[-4 , 1, -5],[ ...

    Text Solution

    |

  15. If A^'=[[3, 4],[ -1, 2],[ 0, 1]] and B=[[-1, 2 , 1],[ 1,2, 3]] ...

    Text Solution

    |

  16. If A^'=[[-2, 3],[ 1, 2]] and B=[[-1, 0],[ 1, 2]], then find (A+2...

    Text Solution

    |

  17. For the matrices A and B verify that, (AB)^'=B^' A^', where i) A=[[1...

    Text Solution

    |

  18. if A=[[sin alpha, cos alpha],[-cos alpha, sin alpha]], then verify A^T...

    Text Solution

    |

  19. show that the matrix A= [[1,-1,5],[-1,2,1],[5,1,3]] is a symmetric mat...

    Text Solution

    |

  20. For the matrix A=[[1 , 5],[ 6 , 7]], verify that i) (A+A^') is a sym...

    Text Solution

    |