Home
Class 12
MATHS
The product of any matrix by the scalar ...

The product of any matrix by the scalar ......... Is the null matrix.

Text Solution

AI Generated Solution

To solve the question, "The product of any matrix by the scalar ......... is the null matrix," we need to understand the concept of scalar multiplication of matrices and the definition of a null matrix. ### Step-by-Step Solution: 1. **Understanding the Null Matrix**: - A null matrix (also known as a zero matrix) is a matrix in which all the elements are zero. For example, a 2x2 null matrix is represented as: \[ \begin{pmatrix} ...
Promotional Banner

Topper's Solved these Questions

  • LINEAR PROGRAMMING

    NCERT EXEMPLAR|Exercise Linear Programming|45 Videos
  • PROBABILITY

    NCERT EXEMPLAR|Exercise Probability|107 Videos

Similar Questions

Explore conceptually related problems

The rank of a null matrix is

If the product of two non null square matrices is a null matrix; show that both of them must be singular matrices.

Multiplication of a matrix by a scalar and its properties

A matrix which is not a square matrix is called a..........matrix.

If an idempotent matrix is also skew symmetric then it can not be 1 an involutary matrix 2 an identity matrix 3 an orthogonal matrix 4 a null matrix.

Give an example of a row matrix which is also a column matrix a diagonal matrix which is not scalar (iii) a triangular matrix.

For any matrix a show that A+A^(T) is symmetric matrix

NCERT EXEMPLAR-MATRICES-Matrices
  1. Sum of two skew-symmetric matrices is always ......... Matrix.

    Text Solution

    |

  2. The negative of a matrix is obtained b y multiplying it by ...........

    Text Solution

    |

  3. The product of any matrix by the scalar ......... Is the null matrix.

    Text Solution

    |

  4. A matrix which is not a square matrix is called a..........matrix.

    Text Solution

    |

  5. Matrix multiplication is distributive over matrix addition

    Text Solution

    |

  6. If A is a symmetric matrix , then A^(3) is a ........ Matrix.

    Text Solution

    |

  7. If A is a skew-symmetric matrix, then A^(2) is a .................

    Text Solution

    |

  8. If A and B are square matrices of the same order, then (i) (AB)=.......

    Text Solution

    |

  9. If A is a skew-symmetric, then kA is a...........(where, k is any scal...

    Text Solution

    |

  10. If A and B are symmetric matrices, then (i) AB-BA is a .......... ...

    Text Solution

    |

  11. If A is symmetric matrix, then B'AB is............

    Text Solution

    |

  12. If A and B are symmetric matrices of same order, then AB is symmetric ...

    Text Solution

    |

  13. In applying one or more row operations while finding A^(-1) by elemen...

    Text Solution

    |

  14. A matrix denotes a number

    Text Solution

    |

  15. Matrices of any order can be added.

    Text Solution

    |

  16. Two matrices are equal. If they have same number of rows and same numb...

    Text Solution

    |

  17. Matrices of different order cannot be subtracted.

    Text Solution

    |

  18. Matrix addition is associative as well as commutative.

    Text Solution

    |

  19. Matrix m ultiplication is commutative.

    Text Solution

    |

  20. A square m atrix where every element is unity is called an identity ma...

    Text Solution

    |