*label*Mathematics

### 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

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

Running head: CONCEPTUAL ASSIGNMENT

Conceptual Assignment

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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...

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