Home
Class 12
MATHS
If A^T=[[3,4],[-1,2],[0,1]] and B=[[-1,2...

If `A^T=[[3,4],[-1,2],[0,1]]` and `B=[[-1,2,1],[1,2,3]]` then verify that
`(A-B)^T=A^T-B^T`

Text Solution

Verified by Experts

`A-B=[[4,-3,-1],[3,0,-2]]`
`(A-B)^T =[[4,3],[-3,0],[-1,-2]]`
`A^T-B^T =[[4,3],[-3,0],[-1,-2]]`
therefore `(A-B)^T=A^T-B^T`
Promotional Banner

Topper's Solved these Questions

  • LINEAR PROGRAMMING

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|40 Videos

  • PROBABILITY

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|318 Videos

Similar Questions

Explore conceptually related problems

If A^'=[[3, 4],[ -1, 2],[ 0, 1]] and B=[[-1, 2 , 1],[ 1,2, 3]] then verify that 1) (A+B)^'=A^'+B^' 2) (A-B)^'=A^'-B^'

If A= [[-1,2,3],[5,7,9],[-2,1,1]] and B= [[-4,1,-5],[1,2,0],[-1,3,1]] then verify that (A-B)^T = A^T-B^T

If A= [[-1,2,3],[5,7,9],[-2,1,1]] and B= [[-4,1,-5],[1,2,0],[-1,3,1]] then verify that (A+B)^T=A^T +B^T

If A^T=[[-2,3],[1,2]] and B^T = [[-1,0],[1,2]] then find (A+2B)^T

If A=[[2, 3],[ 1, -4]] and B=[[1, -2],[ -1, 3]] , then verify that (A B)^(-1)=B^(-1) A^(-1)

If A=[[3 ,sqrt3, 2],[ 4 , 2, 0]] and B=[[2 , (-1), 2],[ 1, 2, 4]] , verify that i. (A^')^'=A ii. (A+B)^'=A^'+B^' iii. (k B)^'=k B^' , where k is any constant.

Let A=[[2,1,3],[4,1,0]] and B=[[1,-1],[0,2],[5,0]] Show that (AB)^T=B^TA^T

Let A=[[1,2,-3],[2,1,-1]] B=[[2,3],[5,4],[1,6]] Verify that (AB)^T=B^TA^T

If A=[[-1, 2, 3],[ 5, 7, 9],[ -2, 1 , 1]] and B=[[-4 , 1, -5],[ 1, 2, 0],[ 1, 3, 1]] then verify that (i) (A+B)^'=A^'+B^'

For the matrices A=[[-1, 2],[ 3, 4]] and B=[[2, 5],[ 3, 6]] , verify that (AB)^(-1)=B^(-1) A^-1?

A N EXCEL PUBLICATION-MATRICES-QUESTION BANK
  1. If A= [[-1,2,3],[5,7,9],[-2,1,1]] and B=[[-4,1,-5],[1,2,0],[-1,3,1]] ...

    Text Solution

    |

  2. If A= [[-1,2,3],[5,7,9],[-2,1,1]] and B=[[-4,1,-5],[1,2,0],[-1,3,1]] ...

    Text Solution

    |

  3. If A^T=[[3,4],[-1,2],[0,1]] and B=[[-1,2,1],[1,2,3]] then verify that ...

    Text Solution

    |

  4. If A^T=[[-2,3],[1,2]] and B^T=[[-1,0],[1,2]] then find (A+2B)^T

    Text Solution

    |

  5. For matrics A and B, verify that (AB)^T=B^T . A^T, where A=[[0],[1],...

    Text Solution

    |

  6. For matrics A and B, verify that (AB)^T=B^T . A^T, where A=[[0],[1],...

    Text Solution

    |

  7. If A^T=[[cosx,sinx],[-sinx,cosx]],Verify that A^TA=I

    Text Solution

    |

  8. if A=[[sin alpha, cos alpha],[-cos alpha, sin alpha]], then verify A^T...

    Text Solution

    |

  9. show that the matrix A= [[1,-1,5],[-1,2,1],[5,1,3]] is a symmetric mat...

    Text Solution

    |

  10. show that the matrix A=[[0,1,-1],[-1,0,1],[1,-1,0]] is a skew symmetri...

    Text Solution

    |

  11. For the matrixA=[[1,5],[6,7]], verify that A+A^T is a symmetric matr...

    Text Solution

    |

  12. For the matrixA=[[1,5],[6,7]], verify that A-A^T is a skew symmetric...

    Text Solution

    |

  13. Find 1/2 (A+A^T) and 1/2(A-A^T) where A=[[0,a,b],[-a,0,c],[-b,-c,0]]

    Text Solution

    |

  14. Write A=[[3,5],[1,-1]] as the sum of a symmetric and a skew symmetric ...

    Text Solution

    |

  15. Express the following matrices as the sum of a Symmetric and a Skew Sy...

    Text Solution

    |

  16. Express the following matrices as the sum of a Symmetric and a Skew Sy...

    Text Solution

    |

  17. Express the following matrics as the sum of a symmetrics and a skew sy...

    Text Solution

    |

  18. If A,B are symmetric matrices of same order then AB-BA is always a ………...

    Text Solution

    |

  19. If A=[[cos alpha, -sin alpha],[sin alpha, cos alpha]], then A+A^T=I if...

    Text Solution

    |

  20. Find P^(-1), if it exists, given P = [(10,-2),(-5,1)]

    Text Solution

    |