Home
Class 12
MATHS
Find the characteristic roots of the two...

Find the characteristic roots of the two-rowed orthogonal matrix `[(cos theta,-sin theta),(sin theta,cos theta)]` and verify that they are of unit modulus.

Text Solution

AI Generated Solution

To find the characteristic roots of the orthogonal matrix \[ A = \begin{pmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{pmatrix} \] ...
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    CENGAGE ENGLISH|Exercise CAE 13.1|5 Videos
  • MATRICES

    CENGAGE ENGLISH|Exercise CAE 13.2|6 Videos
  • MATRICES

    CENGAGE ENGLISH|Exercise Single correct Answer|34 Videos
  • MATHMETICAL REASONING

    CENGAGE ENGLISH|Exercise Archives|10 Videos
  • METHODS OF DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Single Correct Answer Type|46 Videos

Similar Questions

Explore conceptually related problems

Show that the matrix [{:( cos theta , sin theta ),(-sin theta , cos theta ):}] is orthogonal

Evaluate the following: |costheta, -sin theta],[sin theta, cos theta]|

Find the distance between the points : (cos theta, sin theta), (sin theta, cos theta)

Solve sqrt(3) cos theta-3 sin theta =4 sin 2 theta cos 3 theta .

Prove that (cos^3 theta-sin^3 theta)/(cos theta-sin theta) = 1+cos theta sin theta

If A=[[cos 2 theta, sin 2 theta],[-sin2theta, cos2theta]] , find A^2

sin^(3)theta + sin theta - sin theta cos^(2)theta =

(sin theta + sin 2 theta)/( 1 + cos theta + cos 2 theta) = tan theta.

(1+sin2theta+cos2theta)/(1+sin2theta-cos2theta)=?

Find the value of (1+cos theta+sin theta)/(1-cos theta +sin theta)

CENGAGE ENGLISH-MATRICES-ILLUSTRATION
  1. Matrices a and B satisfy AB=B^(-1), where B=[(2,-1),(2,0)]. Find (i...

    Text Solution

    |

  2. Given the matrices A and B as A=[(1,-1),(4,-1)] and B=[(1,-1),(2,-2)]....

    Text Solution

    |

  3. If M is the matrix [(1,-3),(-1,1)] then find matrix sum(r=0)^(oo) ((-1...

    Text Solution

    |

  4. Let p be a non singular matrix, and I + P + p^2 + ... + p^n = 0, then ...

    Text Solution

    |

  5. If A and B are square matrices of same order such that AB=O and B ne O...

    Text Solution

    |

  6. If A is a symmetric matrix, B is a skew-symmetric matrix, A+B is nonsi...

    Text Solution

    |

  7. If the matrices, A, B and (A+B) are non-singular, then prove that [A(A...

    Text Solution

    |

  8. If matrix a satisfies the equation A^(2)=A^(-1), then prove that A^(2^...

    Text Solution

    |

  9. If A and B are non-singular symmetric matrices such that AB=BA, then p...

    Text Solution

    |

  10. If A is a matrix of order n such that A^(T)A=I and X is any matric suc...

    Text Solution

    |

  11. Show that two matrices A=[(1,-1,0),(2,1,1)] and B=[(3,0,1),(0,3,1)] ...

    Text Solution

    |

  12. Using elementary transformations, find the inverse of the matrix : ...

    Text Solution

    |

  13. Let a be a 3xx3 matric such that [(1,2,3),(0,2,3),(0,1,1)]=[(0,0,1),...

    Text Solution

    |

  14. Solve the following system of equations, using matrix method. x+2y+z=7...

    Text Solution

    |

  15. Using matrix method, show that following system of equation is inconsi...

    Text Solution

    |

  16. about to only mathematics

    Text Solution

    |

  17. Find the characteristic roots of the two-rowed orthogonal matrix [(cos...

    Text Solution

    |

  18. Show that if lambda(1), lambda(2), ...., lamnda(n) are n eigenvalues o...

    Text Solution

    |

  19. If A is nonsingular, prove that the eigenvalues of A^(-1) are the reci...

    Text Solution

    |

  20. If one of the eigenvalues of a square matrix a order 3xx3 is zero, the...

    Text Solution

    |