Home
Class 12
MATHS
Let A=[(2,-3),(-7, 5)] and B=[(1, 0),( 2...

Let `A=[(2,-3),(-7, 5)]` and `B=[(1, 0),( 2,-4)]` , verify that `(2A)^T=2A^T` (ii) `(A+B)^T=A^T+B^T` (iii) `(A-B)^T=A^T-B^T` (iv) `(A B)^T=B^T\ A^T`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • ADJOINTS AND INVERSE OF MATRIX

    RD SHARMA ENGLISH|Exercise All Questions|181 Videos
  • ALGEBRA OF VECTORS

    RD SHARMA ENGLISH|Exercise All Questions|325 Videos

Similar Questions

Explore conceptually related problems

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

If A={:[(-1),(2),(3)]:} and B=[-2" "-1" "-4] then verify that (AB)^(T)=B^(T)A^(T).

If A=[[3] , [ 5] , [2] ] and B=[1\ \ 0\ \ 4] , verify that (A B)^T=B^T\ A^Tdot

Let A=[[1,-1, 0],[ 2, 1, 3],[ 1, 2, 1]] a n d B=[[1 ,2, 3],[ 2, 1, 3],[ 0, 1, 1]]dot Find A^T ,B^T and verify that (i) (A+B)^T=A^T+B^T (ii) (A B)^T=B^T A^T (iii) (2A)^T=2A^T

.If A=[[1,4,7],[2,5,8]] and B=[[-3,4,0],[4,-2,-1]] then show that (A+B)^T=A^T+B^T

For the matrices A and B , A=[[2 ,1 ,3 ] , [4 ,1 ,0 ]] , B=[[1 , -1] , [ 0, 2 ] , [ 5 , 0]] verify that (A B)^T=B^T\ A^T

If A^T=[[3, 4],[-1, 2], [0 ,1]] and B=[[-1, 2, 1],[ 1, 2, 3]], find A^T-B^T

If A=[(0,-1,2),(1,0,3),(-2,-3,0)], then A+2A^t equals (A) A (B) -A^t (C) A^t (D) 2A^2

If matrix A=[{:(,2,1,3),(,4,-3,2):}] and B=[{:(,3,-2),(,7,4):}] , find transpose matrices A^t and B^t . If possible, find (i) A+A^t (ii) B+B^t

Consider the matrices A=[(4,6,-1),(3,0,2),(1,-2,5)], B=[(2,4),(0,1),(-1,2)], C=[(3),(1),(2)] Which of the following are defined? (a) (A B)^t C (b) C^T C(A B)^T (c) C^T A B (d) A^T A B B^T C

RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. If A=[(1 2 2)[, (2 1 -2),(a 2 b)] is a matrix satisfying A A^T=9I3 , t...

    Text Solution

    |

  2. Find the values of x,y,z if the matrix A=[[0,2y,z],[x,y,-z],[x,-y,z]] ...

    Text Solution

    |

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

    Text Solution

    |

  4. If A=[[3] , [ 5] , [2] ] and B=[1\ \ 0\ \ 4] , verify that (A B)^T=B^T...

    Text Solution

    |

  5. Let A=[1-1 0 2 1 3 1 2 1]a n dB=[1 2 3 2 1 3 0 1 1]dot Find A^T ,B^T a...

    Text Solution

    |

  6. If A=[[-2],[4], [5]], B=[[1 ,3,-6]], verify that (A B)' = B'A'.

    Text Solution

    |

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

    Text Solution

    |

  8. For the matrices A and B , A=[[2 ,1 ,3 ] , [4 ,1 ,0 ]] , B=[[1 , -1] ,...

    Text Solution

    |

  9. For two matrices A and B , verify that (A B)^T=B^T\ A^T , where A=[[1 ...

    Text Solution

    |

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

    Text Solution

    |

  11. If A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] , then verify that A^T...

    Text Solution

    |

  12. If A=[[sinalpha,cosalpha],[-cosalpha,sinalpha]], verify that A^T A=I2

    Text Solution

    |

  13. Let li,mi,ni; i=1,2,3 be the direction cosines of three mutually perpe...

    Text Solution

    |

  14. Show that the elements on the main diagonal of a skew-symmetric mat...

    Text Solution

    |

  15. If the matrix A=[[0,a,-3],[2,0,-1],[b,1,0]] is skew-symmetric, find ...

    Text Solution

    |

  16. Let A be a square matrix. Then prove that (i) A + A^T is a symmetric m...

    Text Solution

    |

  17. Prove that every square matrix can be uniquely expressed as the sum of...

    Text Solution

    |

  18. If A and B are symmetric matrices, then show that A B is symmetric i...

    Text Solution

    |

  19. Show that the matrix B^T\ A B is symmetric or skew-symmetric accord...

    Text Solution

    |

  20. Let A and B be symmetric matrices of same order. Then AB-BA is a skew ...

    Text Solution

    |