Linear algebra is a useful tool with many applications in computer science. This article will cover the various applications of linear algebra in computer science, including: Internet search, graphics, speech recognition, and artificial intelligence. One of the main focuses of linear algebra in computer science is Internet searches, which involves finding techniques to effectively store and search information. . Linear algebra is used in organizing and sorting these web pages when they are stored in an Internet search database. The vector space model is used to improve search results by representing them as two vectors, the document vector and the query vector. Each dimension in the vector corresponds to a different term. If the term occurs in the document, its value in the vector is a non-zero value. Several ways have been developed to calculate term weights, one of which is the frequency-inverse document frequency (tf-idf) weight. The frequency portion if td-idf refers to the frequency of the term within the document. Inverse document frequency is the logarithmic function of the total number of documents / divided by the number of documents in which the term appears. The inverse frequency document model simply multiplies these 2 values. Using cosine similarity between the document and the query vector allows the computer to group the data or generate similar data. The main advantage of using this model over the standard Boolean model is that it allows you to classify documents based on their relevance and allows partial matching. There are a large number of variations of... middle of paper... in statistical machine learning are probability distributions and parameter spaces represented using vectors. Currently the use of linear algebra within AI can be avoided when using prepared libraries, but to understand how and why algorithms work in the AI ​​unit you will need linear algebra. Linear algebra has a great impact on the field of computer science and is one of the most important tools to learn if you want to excel in computer science. Linear algebra has its effects in a large number of applications in computing, but some of the most significant impacts are its use to organize and sort large quantities of web pages in the Internet search database, its ability to transform images graphics, its impact on speech recognition and, finally, its ability to provide artificial intelligence with the concept of statistical machine learning.