# How do i find the basis of subspace U

1. Dec 6, 2008

### subopolois

1. The problem statement, all variables and given/known data
In this case find the basis of subspace U
1 2 3 4
5 6 7 8
-6 -8 -10 12

2. Relevant equations
elementary row operations

3. The attempt at a solution
alright, so i know i have to reduce the matrix and i have done so
1 2 3 4
0 1 2 3
0 0 0 1
now the answer i get is
[1 5 -6]^T [2 6 -8]^T [4 8 12]^T
but the answer in the back of my text book is
[1 5 -6]^T [2 6 8]^T
what have i done wrong, it seems they have one less column, is it my reduction of the matrix?

2. Dec 6, 2008

### stegz

You just had an error in reducing your matrix somewhere. Check over your work, because the matrix should have been
1 0 -1 -2
0 1 2 3
0 0 0 0
it was probably a simple algebra mistake.

3. Dec 7, 2008

### HallsofIvy

Staff Emeritus
What "subspace U" are you talking about? You give an array of numbers which you refer to as a matrix. I can think of 4 different subspaces that might be meant here:

The row space of the matrix.
The column space of the matrix.
The null space (kernel) of the matrix.
The image of the matrix.

Since you are row-reducing the matrix, you probably mean the column space but it would be a good idea to say so!