Home
Class 12
MATHS
F(x) =[[cos x, -sin x, 0],[ sin x, co...

`F(x) =[[cos x, -sin x, 0],[ sin x, cos x, 0],[ 0, 0, 1]]` Show that `F(x) F(y)=F(x+y)`

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 F(x) = [(cos x, - sin x, 0),(sin x, cos x, 0),(0,0,1)] and G(y) = [(cos y, 0, sin y),(0,1,0),(-sin y, 0, cos y)] then [F(x) G(y)]^(-1) is equal to a) F (-x) G(-y) b) G(-y) F(-x) c) F(x^(-1))G(y^(-1)) d) G(y^(-1))F(x^(-1))

If y=3 cos (log x)+4 sin (log x) Show that x^2 y_2+x y_1+y=0

If x=a^(sin^(-1)t) , y=a^(cos^(-1)t) , a>0 , show that dy/dx=-y/x

(a)Let f(x)={(x,if x is an integer),(0,if x is not an integer)) .Show that underset (x rarr 1)Lt f(x)=0 .

If f(x) = sin x + cos x, x in (-oo, oo) and g(x) = x^(2), x in (-oo, oo) , then (fog)(x) is equal to a)1 b)0 c) sin^(2) (x) + cos (x^(2)) d) sin (x^(2)) + cos (x^(2))

V PUBLICATION-MATRICES-QUESTION BANK
  1. If x[[2],[3]]+y[[-1],[1]]=[[10],[5]] find the values of x and y.

    Text Solution

    |

  2. Given 3[[x,y],[z,w]]=[[x,6],[-1,2w]]+[[4, x+y],[z+w, 3]] find the va...

    Text Solution

    |

  3. F(x) =[[cos x, -sin x, 0],[ sin x, cos x, 0],[ 0, 0, 1]] Show ...

    Text Solution

    |

  4. Show that i) [[5 , (-1)],[ 6, 7]][[2, 1],[ 3 ,4]] ne[[2 , 1 ],[3 ,...

    Text Solution

    |

  5. Find A^2-5 A+6 I, if A=[[2, 0, 1],[ 2 ,1 , 3],[ 1, -1, 0]]

    Text Solution

    |

  6. If A=[[1, 0, 2],[ 0, 2, 1],[ 2, 0, 3]], prove that A^3-6 A^2+7...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |