# linear algebra – Show the maximum number of linearly independent \$n\$-vectors is \$n\$

Show the maximum number of $$n$$-vectors that can be linearly independent is $$n$$.

$$n$$ referring to the order of the vector, take $$n$$ linearly independent $$n$$-vectors. Take any other vector. It’s possible to write the vector as a linear combination of the $$n$$ linearly independent vectors, so $$v_{n+1}=a_1v_1+a_2v_2+dots+a_nv_n$$. Then we have $$a_1v_1+a_2v_2+dots+a_nv_n-v_{n+1}=0$$ and the vectors are linearly dependent. Thus $$n$$ is the maximum number of linearly independent $$n$$-vectors.

I apologize if this is trivial, but I wanted to verify it nonetheless.