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I would reccomend describing in more details. For instance, are you using a server to login. If that is the case and each computer still has its own admins, your method is efficient, assuming you are using the administrator database as a relational value and not a separate list(see below for clarification). If the computers use a server and admins are consistent across computers, this should be unneccesary. If the computers don't use a server, then any particular user exists for only one computer and a true/false column can be set for administrator within your user table.
Clarification: to efficiently run queries, you will need to use an administrator table (more properly named as a status table which I will use for the rest of this). You may use this for multiple statuses (reg, power, admin) or a single status via a true/false column for just admin. Your two other columns in the table will be used to link a computer account with a machine (that way you can keep track of which users use which machines also).
I hope this helps
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