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## Main Question or Discussion Point

What could we say if a matrix is invertible? Could we say that it can span and is linearly independent?

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What could we say if a matrix is invertible? Could we say that it can span and is linearly independent?

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HallsofIvy

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If so, then, yes, a matrix is invertible if and only if its columns (equivalently, rows)

But I still don't know what you mean by "can span". Can span what? Any set of vector spans

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