Let
A basis for the null space of is
You should be able to explain and justify your answer. Enter a coordinate vector, such as \( \verb+<1,2,3>+ \), or a comma separated list of coordinate vectors, such as \( \verb+<1,2,3>,<4,5,6>+ \).
The dimension of the null space of is
because (select all correct answers -- there may be more than one correct answer):
A.
Two of the three columns in have pivots.
B.
has one free variable column.
C.
has a pivot in every row.
D.
Two of the three columns in do not have a pivot.
E.
has two free variable columns.
F.
The basis we found for the null space of has two vectors.
G.
is the identity matrix.
The null space of is a subspace of
because
choose
A has 3 columns
A has 3 rows
.
The geometry of the null space of is
choose
R
R^2
R^3
the origin inside R^3
a 1-dimensional line through the origin inside R^3
a 2-dimensional plane through the origin inside R^3
3-dimensional space
.