Find a basis for the span of a set of vectors

$\begingroup$

Question 1

Find bases for the spans of the following sets.

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

a)

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

Expected answer:

Score: 0/2

Show feedback

This feedback is based on your last submitted answer. Save your changed answer to get updated feedback.

Or, you could:

There's nothing more to do from here.

b)

$\var{code(shown_words[1])} \subset \mathbb{Z}_{\var{field_size[1]}}^{\var{word_length[1]}}$

Expected answer:

Score: 0/2

Show feedback

This feedback is based on your last submitted answer. Save your changed answer to get updated feedback.

Or, you could:

There's nothing more to do from here.

c)

$\var{code(shown_words[2])} \subset \mathbb{Z}_{\var{field_size[2]}}^{\var{word_length[2]}}$

Expected answer:

Score: 0/2

Show feedback

This feedback is based on your last submitted answer. Save your changed answer to get updated feedback.

Or, you could:

There's nothing more to do from here.

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.

$\endgroup$

Numbas has failed

Find a basis for the span of a set of vectors

a)

b)

c)

Advice

a)

b)

c)