Explore BrainMass
Share

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

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

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.

© BrainMass Inc. brainmass.com March 21, 2019, 11:50 pm ad1c9bdddf
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