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    Row Space, Column Space, and Null Space of a Matrix

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    Let M = (1 2 1)
    (0 3 2)
    (-2 6 -1)
    (-4 1 2)

    Find the row space, the column space, and the null space of M, and give their dimensions.

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    https://brainmass.com/math/matrices/row-space-column-space-null-space-matrix-475572

    Solution Preview

    We are given the matrix

    We wish to find the row space, column space, and null space of M, and give their dimensions.

    The row space of M is the vector space spanned by the rows of M. To find this vector space, we perform row reduction on M.
    Adding twice the first row to the third yields
    .
    Adding ...

    Solution Summary

    We find bases for the row space, column space, and null space of a given matrix.

    $2.19