In this problem, the subspace in question is the nullspace of Ax=0. It is an elementary linear algebra problem to find the parametric solution for the system Ax=0. The vectors you get there will span the nullspace.
I just need to know how to start this... I'm looking through my notes but can't figure out how to begin. The wording is also a little bit confusing.
Find a finite subset of each of the following subspaces for which the subspace is the span of the subset.
{x bar is an element of R^{3} such that A(x bar) = theta bar} where A=
1 1 2 1 -1 and theta bar is the zero vector in R^{3}.
2 2 1 2 -1
3 3 2 3 -1
okay, what I did was the following:
Let the matrix
a
b
c be an element of U. Then the matrix:
d
e
1 1 2 1 -1 a 0
2 2 1 2 -1 X b = 0
3 3 2 3 -1 c 0
d
e
Then put that in an augmented matrix and row reduced to get
1 1 0 1 0
0 0 1 0 0
0 0 0 0 1
I got that e=0 and c=0 but now I don't know where to go or even if I'm doing this the right way
This translates to the equations and as you have noted. ThenThen put that in an augmented matrix and row reduced to get
1 1 0 1 0
0 0 1 0 0
0 0 0 0 1
with free. Since every is of this form, it follows that the two vectors I wrote down above span the nullspace of A.