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 \( \verb+<1,2,3,4>+ \), or a comma separated list of coordinate vectors, such as \( \verb+<1,2,3,4>,<5,6,7,8>+ \).
The dimension of the null space of is
because (select all correct answers -- there may be more than one correct answer):
A.
Three of the four columns in have pivots.
B.
Two of the four columns in do not have a pivot.
C.
The basis we found for the null space of has two vectors.
D.
is the identity matrix.
E.
has a pivot in every row.
F.
has one free variable column.
G.
has two free variable columns.
The null space of is a subspace of
because
choose
A has 4 columns
A has 4 rows
.
The geometry of the null space of is
choose
R
R^2
R^3
R^4
the origin inside R^4
a 1-dimensional line through the origin inside R^4
a 1-dimensional line through the origin inside R^2
a 2-dimensional plane through the origin inside R^4
a 3-dimensional subspace of R^4
.