Home
Class 12
MATHS
For the following pair of matrix verif...

For the following pair of matrix verify that `(A B)^(-1)=B^(-1)A^(-1)` . `A=[(3, 2),( 7 ,5)]` and `B=[(6, 7),( 8, 9)]`

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

For the following pair of matrix verify that (A B)^(-1)=B^(-1)A^(-1) . A=[2 1 5 3] and B=[4 5 3 4]

Let A=[(3, 2),( 7, 5)] and B=[(6, 7),( 8, 9)] . Find (A B)^(-1)

If A=|[3, 2], [7, 5]| and B=|[6 ,7], [8, 9]| , verify that (A B)^(-1)=B^(-1)A^(-1) .

Find the distance between the following pairs of points : (i) (2, 3), (4, 1) (ii) (– 5, 7), (– 1, 3) (iii) (a, b), (– a, – b)

Find the matrix A such that : [(1 ,0 ),(0 ,1)]A=[(3 ,3 ,5 ),(1, 0 ,1)] (ii) A[(1, 2, 3 ),(4, 5 ,6)]=[(-7,-8,-9 ),(2, 4 ,6)]

If A=[(2 ,3,-5 ),(1, 2,-1)] and B=[(0, 5,1),(-2, 7, 3)] , find A+B and A-B

Express the following as improper fractions : (a) (7) 3/4 (b) (5) 6/7 (c) (2) 5/6 (d) (10) 3/5 (e) (9) 3/7 (f) (8) 9/4

Show the following pairs of sets by Venn diagrams . A = {1,3,5,7,9} and B = {0,2,4,6,8,10}

Find the distance between the following pair of points: (-6,\ 7) and (-1,\ -5) (ii) (a+b ,\ b+c) and (a-b ,\ c-b)

Find the mode in each of the following data collection. 8,6,7,6,5,4, (1)/(2), 7 (1)/(2), 6 (1)/(2), 8 (1)/(2), 10,7,5,5(1)/(2), 8,9 7,5,6,8 (1)/(2),6

RD SHARMA ENGLISH-ADJOINTS AND INVERSE OF MATRIX-All Questions
  1. Find the inverse following matrix and verify that A^(-1)A=I3 . [(1, ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. Let A=[(3, 2),( 7, 5)] and B=[(6, 7),( 8, 9)] . Find (A B)^(-1)

    Text Solution

    |

  6. Given =[(2,-3),(-4, 7)] , compute A^(-1) and show that 2A^(-1)=9I-A .

    Text Solution

    |

  7. If A=[(4, 5),( 2 ,1)] , then show that A-3I=2(I+3A^(-1))

    Text Solution

    |

  8. Find the inverse of the matrix A=[(a, b),( c,(1+b c)/a)] and show th...

    Text Solution

    |

  9. Given A=[(5, 0, 4),( 2, 3, 2),( 1, 2, 1)] , B^(-1)=[(1, 3, 3),( 1, 4, ...

    Text Solution

    |

  10. Let F(alpha)=[cosalpha-sinalpha0sinalphacosalpha0 0 0 1] and G(beta)=[...

    Text Solution

    |

  11. If A=[(2, 3),( 1, 2)] , verify that A^2-4A+I=O , where I=[(1, 0),( 0, ...

    Text Solution

    |

  12. Show that A=[(-8, 5),( 2, 4)] satisfies the equation A^2+4A-42 I=O . H...

    Text Solution

    |

  13. If A=[(3, 1),(-1 ,2)] , show that A^2-5A+7I=O . Hence, find A^(-1) .

    Text Solution

    |

  14. If A=[(4 ,3 ),(2 ,5)] , find x and y such that A^2-x A+y I=O .

    Text Solution

    |

  15. If A=[(3,-2),( 4,-2)] , find the value of lambda so that A^2=lambdaA-2...

    Text Solution

    |

  16. Show that A=[(5, 3),(-1,-2)] satisfies the equation x^2-3x-7=0 . Thus,...

    Text Solution

    |

  17. Show that A=[(6, 5),( 7, 6)] satisfies the equation x^2-12 x+1=0 . Thu...

    Text Solution

    |

  18. For the matrix A=[1 1 1 1 2-3 2-1 3] . Show that A^3-6A^2+5A+11\ I3=O ...

    Text Solution

    |

  19. Show that the matrix, A=[[1, 0,-2],[-2,-1, 2],[ 3, 4, 1]] satisfies th...

    Text Solution

    |

  20. If A=[2-1 1-1 2-1 1-1 2] . Verify that A^3-6A^2+9A-4I=O and hence find...

    Text Solution

    |