Information retrieval (IR) system is a system, which is used to search and retrieve information relevant to the users’ needs. IR system retrieves and displays documents that are relevant to the users’ input (query). The information retrieval system has several steps and must execute the steps in order to obtain query results. The steps consist of two processes. The first one is processing query and the second one is processing the document collection. Processing query includes: conduct text operation, query formulation, and make terms index for query. Processing the document collection includes: conduct text operation, indexing, and make collection index for document collection. Obtaining terms index and collection index, we are able to process terms index and collection index to obtain ranking results. To obtain ranking results requires knowledge from basic linear algebra. This paper also explores how to make ranking from the most relevant documents to the most irrelevant documents.
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