Let M = (1 2 1)
(0 3 2)
(-2 6 -1)
(-4 1 2)
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
We find bases for the row space, column space, and null space of a given matrix.