True or false? The nullspace of the identity matrix contains only the origin.

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degeneratecircle eNotes educator| Certified Educator

This is true. The nullspace of the `nxxn` identity matrix `I_n` is the set of all vectors `vecx` that satisfy `I_nvecx=vec0.` But `I_nvecx=vecx,` so this is only true if `vecx=vec0.` Thus the nullspace is only the zero vector, i.e., the origin.