What does 'Linearly independent solution' and 'Linearly dependent solution' mean in terms of Matrix Algebra?
2026-04-03 02:31:40.1775183500
Linearly Independent solutions.
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I trust that you know what it means for a set of vectors to be linearly independent, and what it means for a set of vectors to be linearly dependent. (If not, then that's the question you should be asking)
Now, if $A$ is a matrix, and you have a few solutions of the equation $Ax=0$, then you can ask whether those solutions – those vectors that you have found – are linearly dependent or linearly independent.