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I am new to the forums. I will try and keep this short.

Linear Independence vs Linear Dependence. It's easier to understand from a vector perspective but when it's brought back to a system of equations, I get twisted in symantics.

(1) Consistent: Linearly independent vs Linearly dependent. If it's consistent, it has one or more solutions: Linear independent (one solution). Linear dependent (infinite solutions). Linear independent also means equations can't be expressed as a linear combination of the others. If they are Linear dependent, they can.

(2) Inconsistent: Linearly independent vs Linearly dependent. Since inconsistent means no solutions. You can't label a system of equations as linearly independent/dependent since both means a solution exists.

I thought I had all this straight until I read a paper here. This gentleman quotes James/James, Mathematics Directory as his source and doesn't seem to agree with (2).

If anyone can untangle me, I would appreciate it.

Anthony

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# Linear Independence/Dependence

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