Find a basis for the span of a set of vectors

Error

There was an error loading the page.

Contributors

Feedback

From users who are members of Content created by Newcastle University :

Newcastle University Mathematics and Statistics

said

Ready to use

6 years, 8 months ago

History

○

Christian Lawson-Perfect 6 years, 8 months ago

Published this.

○

Newcastle University Mathematics and Statistics 6 years, 8 months ago

Gave some feedback: Ready to use

○

Christian Lawson-Perfect 6 years, 8 months ago

Created this.

There is only one version of this question that you have access to.

Question statement

Find bases for the spans of the following sets.

Enter each answer as a list of vectors separated by commas.

Give any introductory information the student needs.

			Name	Type	Generated Value

num_parts	integer	3
field_size	list	[ 5, 2, 2 ]
word_length	list	[ 4, 6, 6 ]
generating_set	list	Nested 3×4 list
span	list	List of 3 items
shown_words	list	List of 3 items
codeword_matrix	list	List of 3 items
rref	list	List of 3 items
rref_matrix	list	List of 3 items
basis	list	Nested 3×4 list

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
3

JME function reference

Description

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

Can an exam override the value of this variable?

Generated value: `integer`

→ Used by:

basis
field_size
generating_set
shown_words
word_length

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Match text pattern
  Add
Part b) Gap-fill
1. Gap Match text pattern
  Add
Part c) Gap-fill
1. Gap Match text pattern
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

$\var{code(shown_words[0])} \subset \mathbb{Z}_{\var{field_size[0]}}^{\var{word_length[0]}}$

Unnamed gap

Advice

a)

We can find a basis by forming a matrix whose rows are the given vectors:

\[ \var{codeword_matrix[0]} \]

Row-reduce this matrix to obtain the echelon form

\[ \var{rref_matrix[0]} \]

Take the non-zero rows of this matrix as a set of basis vectors, i.e. $\var{latex(join(map(latex(x),x,basis[0]),', '))}$. This is only one of many possible bases for the given vectors.

b)

We can find a basis by forming a matrix whose rows are the given vectors:

\[ \var{codeword_matrix[1]} \]

Row-reduce this matrix to obtain the echelon form

\[ \var{rref_matrix[1]} \]

Take the non-zero rows of this matrix as a set of basis vectors, i.e. $\var{latex(join(map(latex(x),x,basis[1]),', '))}$. This is only one of many possible bases for the given vectors.

c)

We can find a basis by forming a matrix whose rows are the given vectors:

\[ \var{codeword_matrix[2]} \]

Row-reduce this matrix to obtain the echelon form

\[ \var{rref_matrix[2]} \]

Take the non-zero rows of this matrix as a set of basis vectors, i.e. $\var{latex(join(map(latex(x),x,basis[2]),', '))}$. This is only one of many possible bases for the given vectors.

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Match text pattern
Match text pattern		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Match text pattern
Match text pattern		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Match text pattern
Match text pattern		Hasn't run yet

This question is used in the following exams:

Loading...

Error

Find a basis for the span of a set of vectors

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

Gap-fill

a)

b)

c)

Loading...

Error

Find a basis for the span of a set of vectors

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

Gap-fill

a)

b)

c)

Generated value: `integer`