List all vectors in spanning set

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Christian Lawson-Perfect 6 years, 8 months ago

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Newcastle University Mathematics and Statistics 6 years, 8 months ago

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Christian Lawson-Perfect 6 years, 8 months ago

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Question statement

List all of the vectors in the following spans.

Enter each answer as a list of vectors, separated by commas. For example, 000,001,002.

Give any introductory information the student needs.

			Name	Type	Generated Value

num_parts	integer	3
field_size	list	[ 3, 3, 2 ]
word_length	list	[ 4, 6, 6 ]
num_words	list	[ 2, 2, 3 ]
generators	list	List of 3 items
spanning_set	list	List of 3 items
generated_code	list	List of 3 items

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
3

JME function reference

Description

Number of parts in the question (i.e., number of spanning sets to generate)

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `integer`

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$\var{latex(show_span(generators[0]))} \subset \mathbb{Z}_{\var{field_size[0]}}^{\var{word_length[0]}}$

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a)

$\var{show_span(generators[0])}$ is the set of all linear combinations of the vectors $\var{join_words(generators[0])}$.

Every vector in the span is the sum of {join(list(0..field_size[0]-2),',')} or {field_size[0]-1} times each of the given vectors. That is, every vector in the span has the form

\[ w = \var{latex(join(map('\\lambda_{j+1} \\times \\mathtt{'+generators[0][j]+'}',j,0..num_words[0]-1),'+'))} \]

The set of vectors in the span is thus

\[ \var{latex(join_words(spanning_set[0]))} \]

b)

$\var{show_span(generators[1])}$ is the set of all linear combinations of the vectors $\var{join_words(generators[1])}$.

Every vector in the span is the sum of {join(list(0..field_size[1]-2),',')} or {field_size[1]-1} times each of the given vectors. That is, every vector in the span has the form

\[ w = \var{latex(join(map('\\lambda_{j+1} \\times \\mathtt{'+generators[1][j]+'}',j,0..num_words[1]-1),'+'))} \]

The set of vectors in the span is thus

\[ \var{latex(join_words(spanning_set[1]))} \]

a)

$\var{show_span(generators[2])}$ is the set of all linear combinations of the vectors $\var{join_words(generators[2])}$.

Every vector in the span is the sum of {join(list(0..field_size[2]-2),',')} or {field_size[2]-1} times each of the given vectors. That is, every vector in the span has the form

\[ w = \var{latex(join(map('\\lambda_{j+1} \\times \\mathtt{'+generators[2][j]+'}',j,0..num_words[2]-1),'+'))} \]

The set of vectors in the span is thus

\[ \var{latex(join_words(spanning_set[2]))} \]

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Taxonomy: mathcentre

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Christian Lawson-Perfect 6 years, 8 months ago

Newcastle University Mathematics and Statistics 6 years, 8 months ago

Christian Lawson-Perfect 6 years, 8 months ago

Error in variable testing condition

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Generated value: `integer`

Parts

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a)

b)

a)

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List all vectors in spanning set

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 6 years, 8 months ago

Newcastle University Mathematics and Statistics 6 years, 8 months ago

Christian Lawson-Perfect 6 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Match text pattern

Advanced settings

a)

b)

a)

Generated value: `integer`