Home
Class 12
MATHS
If Aalpha=[[cosalpha ,sinalpha],[-sinalp...

If `A_alpha=[[cosalpha ,sinalpha],[-sinalpha,cosalpha]]` , then prove that `A_alphaA_beta=A_(alpha+beta)` for every positive integer `n` .

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • ADJOINTS AND INVERSE OF MATRIX

    RD SHARMA ENGLISH|Exercise All Questions|181 Videos
  • ALGEBRA OF VECTORS

    RD SHARMA ENGLISH|Exercise All Questions|325 Videos

Similar Questions

Explore conceptually related problems

If A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] is such that A^T=A^(-1) , find alpha

If A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] is such that A^T=A^(-1) , find alpha .

If f(alpha)=[[cosalpha,-sinalpha,0],[sinalpha,cosalpha,0],[ 0, 0, 1]],t h e n prove that [F(alpha)]^(-1)=F(-alpha)dot

Let A_(alpha)=[(cosalpha, -sinalpha,0),(sinalpha, cosalpha, 0),(0,0,1)] , then :

Prove that |cosalpha-cosbeta|lt=|alpha-beta|

If A=[(cosalpha,sinalpha),(-sinalpha,cosalpha)] prove that A.A^(T)=1 Hence find A^(-1)

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

If A_alpha=[cosalphasinalpha-sinalphacosalpha] , then prove that (A_alpha)^n=[cos n\ alphasinn\ alpha-sinn\ alpha cos n\ alpha] for every positive integer n .

If A= [[cosalpha,sinalpha],[-sinalpha,cosalpha]] then show that A^2=[[cos2alpha,sin2alpha],[-sin2alpha,cos2alpha]]

If cosalpha+cosbeta=0=sinalpha+sinbeta , then prove that cos2alpha +cos2beta=-2cos(alpha +beta) .

RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. If A=[3 1-1 2], show that A^2-5A+7I=0

    Text Solution

    |

  2. Prove the following by principle of mathematical induction If A=[[3,-4...

    Text Solution

    |

  3. If Aalpha=[[cosalpha ,sinalpha],[-sinalpha,cosalpha]] , then prove tha...

    Text Solution

    |

  4. If Aalpha=[cosalphasinalpha-sinalphacosalpha] , then prove that (Aalph...

    Text Solution

    |

  5. If a is a non-zero real or complex number. Use the principle of mat...

    Text Solution

    |

  6. If A=[(1 1 1),( 1 1 1),( 1 1 1)] , then prove that A^n=|(3^(n-1)3^(n-1...

    Text Solution

    |

  7. Under what conditions is the matrix equation A^2-B^2=(A-B)(A+B) is ...

    Text Solution

    |

  8. If A is any mxxn such that A B and B A are both defined show that B...

    Text Solution

    |

  9. A ,\ B are two matrices such that A B and A+B are both defined; sho...

    Text Solution

    |

  10. If A and B are square matrices of order n , then prove that A and B...

    Text Solution

    |

  11. If A B=A and B A=B , then show that A^2=A , B^2=B .

    Text Solution

    |

  12. Give an example of two matrices A and B such that A!=O ,\ \ B!=O ,\ ...

    Text Solution

    |

  13. Give an example of three matrices A ,\ B ,\ C such that A B=A C but...

    Text Solution

    |

  14. There are 2 families A and B. There are 4 men, 6 women and 2 children ...

    Text Solution

    |

  15. Use matrix multiplication to divide Rs. 30,000 in two parts such that ...

    Text Solution

    |

  16. Three schools A ,\ B and C organised a mela for collecting funds fo...

    Text Solution

    |

  17. Prove that the product of matrices [cos^2thetacosthetasinthetacosthe...

    Text Solution

    |

  18. Let A=[(0,-tan(alpha/2)),(tan(alpha/2),0)] and I be the identity matr...

    Text Solution

    |

  19. Let F(x)=[cosx -sinx 0 sinx cosx 0 ...

    Text Solution

    |

  20. Let A=[2 3-1 2] and f(x)=x^2-4x+7 . Show that f(A)=O . Use this result...

    Text Solution

    |