Why do some implementations of the simplex method use an identity matrix while others don't?

Question

I am working on an implementation of the simplex method. Ferguson's notes$^\color{magenta}{\star}$ don't include the identity matrix in the simplex tableau. My algorithm$^\color{magenta}{\dagger}$ seems to work (it passes multiple unit tests that compare its output to SciPy's linear programing function). However, every other resource I consult includes an identity matrix (e.g., Simplex method - identity matrix). What's going on? Is it more efficient to implement things without the identity matrix?

Here's an image from the linked PDF that demonstrates what I'm taking about. I also included a worked out example from the PDF.

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References

_{$\color{magenta}{\star}$ Thomas S. Ferguson, Linear Programming — a concise introduction [PDF]}

_{$\color{magenta}{\dagger}$ SymPy, Add linear programing function using simplex method [GitHub pull request]}