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

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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#### 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.

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