So let's say I have "n" linearly independent vectors in "m" dimensions (m > n).
Is it true that the dimension of span of these n vectors is also n?
And if I find a vector orthogonal to all the n vectors, what will be the span of combined system of the n vectors and the orthogonal vector? n+1?
If yes, how can I prove it?
2026-03-30 02:07:04.1774836424
What is the dimension of span of a vector orthogonal to 'n' linearly independent vectors?
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