Find a basis for the row space of a matrix

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Christian Lawson-Perfect 6 years, 7 months ago

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Question statement

Find bases for the row spaces of the following matrices.

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

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			Name	Type	Generated Value

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

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2

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$\var{matrix(map(x[0..word_length[0]],x,shown_words[0]))}$ in $\mathbb{Z}_{\var{field_size[0]}}$.

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Advice

a)

We can find a basis by row-reducing the given matrix to 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 row space of the given matrix.

b)

We can find a basis by row-reducing the given matrix to 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 row space of the given matrix.

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Christian Lawson-Perfect 6 years, 7 months ago

Newcastle University Mathematics and Statistics 6 years, 7 months ago

Christian Lawson-Perfect 6 years, 7 months ago

Error in variable testing condition

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Generated value: `integer`

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Find a basis for the row space of a matrix

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 6 years, 7 months ago

Newcastle University Mathematics and Statistics 6 years, 7 months ago

Christian Lawson-Perfect 6 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

Generated value: `integer`