Home
Class 12
MATHS
If A and B are two mxxn matrices and O i...

If A and B are two `mxxn` matrices and O is the null matrix of the type `mxxn`, then show that: `A +B = 0 rArr A = -B and B = -A`

Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MODERN PUBLICATION|Exercise EXERCISE|232 Videos

  • LINEAR PROGRAMMING

    MODERN PUBLICATION|Exercise EXERCISE|156 Videos

  • MOCK TEST-1

    MODERN PUBLICATION|Exercise EXERCISE|33 Videos

Similar Questions

Explore conceptually related problems

If A and B are any two matrics then

If A and B are two matrices such that their product AB is a null matrix, then

If A and B are invertible matrices , then:

If A and B are two matrices of the same order, then A-B=B-A .

If A and B are two square matrices of the same order, then A+B=B+A .

If A and B are two square matrices of the same order, then AB=BA .

If A and B are two matrices such that both A+B and AB are defined, then

If A and B are two invertible matrices, then the inverse of AB is equal to :

For any two matrices A and B, we have

MODERN PUBLICATION-MATRICES-EXERCISE
  1. Verify associative law of matrx addition for the matrices: A = {:[(1...

    Text Solution

    |

  2. If A = {:[(1,2,3),(-1,0,2),(1,-3,-1)], B = [(4,5,6),(-1,0,1),(2,1,2)] ...

    Text Solution

    |

  3. If A and B are two mxxn matrices and O is the null matrix of the type ...

    Text Solution

    |

  4. Find the values of x,y,z and t, if: {:2[(x,z),(y,t)] + 3 [(1,-1),(0,...

    Text Solution

    |

  5. If {:x[(2),(3)] + y [(-1,1)] = [(12),(6)], write the value. Of 'x'.

    Text Solution

    |

  6. If {:2[(3,4),(5,x)] + [(1,y ),(0,1)] = [(7,0),(10,5)], find (x-y).

    Text Solution

    |

  7. Find the vale of (x+y) from the following equation: {:2[(x,5),(7,y-3...

    Text Solution

    |

  8. If A = {:[(4,2,7),(2,1,7)] and B = [(2,1,5),(3,4,6)] find 2A-B.

    Text Solution

    |

  9. If A = {:[(8,0),(4,-2),(3,-6)] and B = [(2,-2),(4,2),(-5,1)], then fin...

    Text Solution

    |

  10. If A = diag. [3,-5,7]^* and B - diag. [-1,2,4], then find (2A + 3B).

    Text Solution

    |

  11. If A = [(2,7),(9,8)] and B = [(1,2),(0,3)], then find: (A-B).

    Text Solution

    |

  12. If A = [(2,3),(-1,4)], find 2A

    Text Solution

    |

  13. If A = [(2,3),(-1,4)], find -3A

    Text Solution

    |

  14. Find 'x' and 'y' if 2{:[(x,5),(3,y)] = [(4,10),(6,6)]

    Text Solution

    |

  15. If A = {:[(4,2,3),(1,5,7)] and B = [(1,3,7),(0,4,1)], find 2A + B.

    Text Solution

    |

  16. If A = {:[(2,-1),(4,2)] and B = [(2,3),(1,2)], find 2A + 3B.

    Text Solution

    |

  17. If A = {:[(1,2,3),(2,3,1)] and B = [(3,-1,3),(-1,0,2)], then find 2A +...

    Text Solution

    |

  18. Find the value of (y-x) from the following equation : 2{:[(x,5),(7,y...

    Text Solution

    |

  19. Find the value of (x+y) from the following equation: 2{:[(1,3),(0,x)...

    Text Solution

    |

  20. If A = {:[(2//3, 1 , 5//3),(1//3, 2//3, 4//3),(7//3, 2, 2//3)] and B =...

    Text Solution

    |