Home
Class 12
MATHS
Find the adjoint of the following matr...

Find the adjoint of the following matrices: `[(-3, 5),( 2, 4)]` Verify that `(a d j\ A)A=|A|I=A(a d j\ A)` for the above matrices.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • ALGEBRA OF MATRICES

    RD SHARMA ENGLISH|Exercise All Questions|410 Videos

Similar Questions

Explore conceptually related problems

Find the adjoint of each of the matrices [{:(1,2),(3,4):}]

Find adjoint of the matrice in [(1,-1, 2),( 2, 3, 5),(-2, 0, 1)]

Find the adjoint of the following matrices: [(cosalpha,sinalpha),(sinalpha,cosalpha)] (ii) [(1,tanalpha//2),(-tanalpha//2, 1)] Verify that (a d j\ A)A=|A|I=A(a d j\ A) for the above matrices.

Compute the adjoint of each of the following matrices: [[1, 2, 2],[ 2 ,1 ,2],[ 2, 2, 1]] (ii) [[1, 2, 5],[ 2, 3,1],[-1, 1, 1]] (iii) [[2,-1, 3],[ 4, 2, 5],[ 0, 4,-1]] (iv) [[2, 0,-1],[ 5, 1, 0],[ 1, 1, 3]] Verify that (a d j\ A)A=|A|I=A(a d j\ A) for the above matrices.

Compute the adjoint of the matrix A given by A=[[1, 4, 5], [3, 2, 6], [0 ,1 ,0]] and verify that A(a d j\ A)=|A|I=(a d j\ A)Adot

Find the adjoint of the matrix A=[(-1,-2,-2), (2 ,1,-2), (2,-2, 1)] and hence show that A(a d j\ A)=|A|\ I_3 .

Find adjoint of the matrice in [(1, 2),( 3, 4)]

Compute the adjoint of the matrix A given by A=[[1, 4, 5],[ 3 ,2, 6],[ 0 ,1, 0]] and verify that A(a d jA)=|A|I=(A d jA)Adot

Find the adjoint of matrix A=[a_(i j)]=[(p, q),( r, s)] .

Verify A (a d j A) = (a d j A) A = |A|I for [(2 ,3),(-4,-6)]

RD SHARMA ENGLISH-ADJOINTS AND INVERSE OF MATRIX-All Questions
  1. If A=[(2,-1, 1),(-1, 2,-1),( 1,-1, 2)] , find (a d j\ A)^(-1) and (a...

    Text Solution

    |

  2. Let A be a non-singular matrix. Show that A^T A^(-1) is symmetric i...

    Text Solution

    |

  3. Find the adjoint of the following matrices: [(-3, 5),( 2, 4)] Verif...

    Text Solution

    |

  4. Find the adjoint of the following matrices: [(cosalpha,sinalpha),(si...

    Text Solution

    |

  5. Compute the adjoint of each of the following matrices: [[1, 2, 2],[ ...

    Text Solution

    |

  6. For the matrix A=[[1,-1, 1],[ 2 ,3, 0 ],[18 ,2 ,10]] , show that A(a d...

    Text Solution

    |

  7. If A=[[-4,-3,-3],[ 1, 0 ,1],[ 4 ,4, 3]] , show that a d j\ A=A .

    Text Solution

    |

  8. If A=[(-1,-2,-2 ),(2, 1,-2),( 2,-2 ,1)] , show that a d j\ A=3A^T .

    Text Solution

    |

  9. Find A(a d j\ A) for the matrix A=[[1,-2 ,3],[ 0, 2,-1],[-4 ,5, 2]] .

    Text Solution

    |

  10. Find the inverse of the following matrix: |[costheta,sintheta],[-sinth...

    Text Solution

    |

  11. Find the inverse of [(1, 2, 3),( 2, 3, 1),( 3, 1, 2)].

    Text Solution

    |

  12. Find the inverse of [(1, 2, 5),( 1,-1,-1),( 2 ,3,-1)]

    Text Solution

    |

  13. Find the inverse of [(2,-1, 1),(-1, 2,-1),( 1,-1, 2)]

    Text Solution

    |

  14. Find the inverse of [(2, 0,-1),( 5, 1, 0),( 0, 1, 3)]

    Text Solution

    |

  15. Find the inverse of [(0 ,1,-1),( 4,-3, 4),( 3,-3, 4)]

    Text Solution

    |

  16. Find the inverse of [(0, 0,-1), (3 ,4 ,5),(-2,-4,-7)]

    Text Solution

    |

  17. Find the inverse of [(1, 0, 0),( 0,cosalpha,sinalpha),(0,sinalpha,-cos...

    Text Solution

    |

  18. Find the inverse following matrix and verify that A^(-1)A=I3 . [(1, ...

    Text Solution

    |

  19. Find the inverse following matrix and verify that A^(-1)A=I3 . [(2, ...

    Text Solution

    |

  20. For the following pair of matrix verify that (A B)^(-1)=B^(-1)A^(-1)...

    Text Solution

    |