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If A=\left [ a_{ij} \right ] is a square matrix of order n\times n  and k is a scalar ,then \left | KA \right |=

  • Option 1)

    K^{n}\left | A \right |

  • Option 2)

    K\left | A \right |

  • Option 3)

    Kn^{-1}\left | A \right |

  • Option 4)

    None

 

Answers (1)

best_answer

As we learned in concept

Scalar multiplication of matrix -

\lambda A=\left [ \lambda a_{ij} \right ]

- wherein

\lambda is multiplied to every element of matrix A

 

 Matrix KA means every element is multiplied by K.  Thus the determinant is multiplied by K^{n}

 


Option 1)

K^{n}\left | A \right |

Correct option

Option 2)

K\left | A \right |

Incorrect option

Option 3)

Kn^{-1}\left | A \right |

Incorrect option

Option 4)

None

Incorrect option

Posted by

divya.saini

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