All solution of AX=0 where A is a n\times n

lovesickgirlsrd5

lovesickgirlsrd5

Answered question

2022-02-25

All solution of AX=0 where A is a n×n matrix and X is a column vector form a subspace of Rn. All the subspaces of Rn are of this type. How to prove this result?

Answer & Explanation

Gene Espinosa

Gene Espinosa

Beginner2022-02-26Added 7 answers

Let S a subspace of Rn and choose (e1,,ep) a basis of S which we compete it by a basis (e1,,ep,ep+1,,en) of Rn.
Now let the endomorphism f defined by
f(ei)=0, 1ip and f(ei)=ei, p+1in and let A the matrix of f in this basis then
AX=0XS

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