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