Conceptual Assignment

Anonymous

Question Description

Recent Concepts:

For this assignment, you will write a document explaining the connections between the following course concepts:

. Spanning set of a vector space

. Linear dependence / independence of a set of vectors

. Basis of a vector space

. Dimension of a vector space

. The 4 subspaces of a matrix

Tutor Answer

Thomas574
School: UC Berkeley

Hello, I'm done, all areas are correctly answered as per your request.

Running head: CONCEPTUAL ASSIGNMENT

Conceptual Assignment
Name
Institution
Instructor
Date

1

2

CONCEPTUAL ASSIGNMENT
Conceptual Assignment
Spanning set of a vector space

A vector is called a spanning set in linear algebra if the smallest subspace that contains the
set is the linear span of a set S. assume that the subset of vector space V is S={v1,v2,...vn}. The
case can be said that S spawns V because every vector contained in the subspace V can be written
in a linear combination of S vectors. The span of a set therefore refers to the set of all linear
combinations of the vectors in the subset, in this case vectors in S if S= {v1,v2,...vn} is set of
vectors in subspace V (Strang, 2008).
What I learn from this relationship is that I can use a subset of the vector space of a vector
to represent all vectors. In this case, I can use the smallest part of V, which is S, to represent all
vectors that are in subspace V. below is the form taken by a linear combination created by vectors
and scalars in the subset S of V. the combination takes; a=k1v1+k2v2+k3v3+...+knvn where K and
V represents the scalars and vectors from the subset respectively (Strang, 2008).
In this case, the vectors that can be reached when S is the subset of vector space V can be
created using this combination. We used (a) to represent the span or the linear combination. The
theorem of the linear relationship however sets that the spann (S) must be a subspace of V as far
as S is a set of vectors in vector space V.
In theoretical terms, the spann (S) must be present at every subspace of V that contains S
since the spann (S) is the smallest subspace that contains vector S= {v1,v2,...vn} in the vector V.
The simplest way to know if a set of vectors spawns a space is by using the Gaussian elimination
and checking whether there are three non-zero rows at the end (Strang, 2008).

3

CONCEPTUAL ASSIGNMENT
Linear dependence/independence set of vectors

In the previous section, we have discussed construction of a spanning set of vector space.
In this section, we can ask what subspace will equal to the whole vector space in the linear
relationship (Strang, 2008).
Let us assume that there are at least two vectors in...

flag Report DMCA
Review

Anonymous
Top quality work from this tutor! I’ll be back!

Anonymous
Just what I needed… fantastic!

Anonymous
Use Studypool every time I am stuck with an assignment I need guidance.

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4

Brown University





1271 Tutors

California Institute of Technology




2131 Tutors

Carnegie Mellon University




982 Tutors

Columbia University





1256 Tutors

Dartmouth University





2113 Tutors

Emory University





2279 Tutors

Harvard University





599 Tutors

Massachusetts Institute of Technology



2319 Tutors

New York University





1645 Tutors

Notre Dam University





1911 Tutors

Oklahoma University





2122 Tutors

Pennsylvania State University





932 Tutors

Princeton University





1211 Tutors

Stanford University





983 Tutors

University of California





1282 Tutors

Oxford University





123 Tutors

Yale University





2325 Tutors