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13 January, 01:33

If A is a 7 x 3 matrix, what is the smallest possible dimension of Nul A? Explain your answer.

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  1. 13 January, 03:19
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    the smallest possible dimension of Nul A is zero.

    Step-by-step explanation:

    The given matrix has 7 rows and 3 columns since it is a 7 x 3 matrix.

    Rank Nullity Theorem:-

    For any matrix A

    rank A + dimension of Nul A = Column of A

    Here, column of A = 3

    Thus, we have

    rank A + dimension of Nul A = 3

    Since, it is a 7 x 3 matrix, hence the rank of this matrix can be 3.

    Therefore, we have

    3 + dimension of Nul A = 3

    => dimension of Nul A = 0

    Therefore, the smallest possible dimension of Nul A is zero.
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