Let
A basis for the column 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 column space of is
because (select all correct answers -- there may be more than one correct answer):
A.
Two of the three columns in do not have a pivot.
B.
has a pivot in every row.
C.
is the identity matrix.
D.
Two of the three columns in have pivots.
E.
Two of the three columns in are free variable columns.
F.
The basis we found for the column space of has two vectors.
The column space of is a subspace of
because
choose
each column of A is a vector in R^3
A has 3 columns
.
The geometry of the column 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
.