Thread: Generating a subspace (dimension, basis)

The following system of vectors generates a subspace. What is the dimension of the generated subspace? Let's show a basis of the subspace. Choose a basis of the subspace from the given generating elements!

[1,1,0,...,0], [0,1,1,0,...,0], ..., [0,0,...1,1], [1,0,...,0,1]

I would be grateful if you could help me!
Thank you in advance!

Originally Posted by zadir

The following system of vectors generates a subspace. What is the dimension of the generated subspace? Let's show a basis of the subspace. Choose a basis of the subspace from the given generating elements!

[1,1,0,...,0], [0,1,1,0,...,0], ..., [0,0,...1,1], [1,0,...,0,1]

I would be grateful if you could help me!
Thank you in advance!

Evidently the dimension is the cardinality of the maximal independent subset of the set of vectors described. So how would you go about finding such a set?