Home
Class 12
MATHS
If A=[[3 ,sqrt3, 2],[ 4 , 2, 0]] and ...

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.

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 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 (i) (A+B)^'=A^'+B^'

If A=[[1 , 2, 3],[ 2, 3 , 1]] and B=[[3, -1, 3],[ -1, 0, 2]] , then find 2 A-B .

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

Given A=[[sqrt3 , 1 , -1], [2 , 3 , 0]] and B=[[[2 , sqrt5 , 1,]] , [[-2, 3 , 1/2]]] , find A+B

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

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

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=[(-1),(2),(3)] and B=[-2 -1 -4] Verify that (AB)^T=B^T.A^T

V PUBLICATION-MATRICES-QUESTION BANK
  1. Assume that X,Y,Z,W and P are matrices of order 2xxn, 3xxk, 2xxp, nx...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. If A^'=[[-2, 3],[ 1, 2]] and B=[[-1, 0],[ 1, 2]], then find (A+2...

    Text Solution

    |

  12. For the matrices A and B verify that, (AB)^'=B^' A^', where i) A=[[1...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. For the matrix A=[[1 , 5],[ 6 , 7]], verify that i) (A+A^') is a sym...

    Text Solution

    |

  16. 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

    |

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

    Text Solution

    |

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

    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

    |