Covered today:
(NOTE: this is not in the book) Vector spaces and Linear systems.
For Next time:
1.
Show that the two conditions in the definition of vector subspace are independent by constructing:
(a)
a subset of two-dimensional space closed under vector addition and even subtraction, but not under scalar multiplication;
(b)
a subset of two-dimensional space closed under scalar multiplication, but not under vector addition.
2.
Which of the following subsets of
are actually subspaces?
(a)
The plane of vectors with first component
.
(b)
The plane of vectors
with
.
(c)
The solitary vector
.
(d)
All linear combinations of the vectors
and
.
3.
Describe the column space and the nullspace of the matrices
and
4.
Let
be the plane in 3-space with equation
. What is the equation of the plane
through the origin parallel to
? Are
and
subspaces of
?
5.
Which descriptions are correct? The solutions
of
form a plane, line, point, subspace, nullspace of
, column space of
.
6.
Show that the set of nonsingular
matrices is not a vector space. Also show that the set of singular
matrices is not a vector subspace.
About this document ...
Math 9 Fall 2000 2000-10-23