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