This paper systematically presents a specific application of linear algebra in information security and cryptography, highlighting the crucial role of matrix operations and linear techniques in the design and analysis of encryption algorithms. Specifically, we focus on a method that utilizes linear algebra to enhance the security and efficiency of modern cryptographic systems. A detailed illustrative example is provided to help readers better understand how these mathematical tools are applied in practice. Furthermore, we review existing encryption techniques and propose a new matrix-based scheme that leverages linear algebra to improve data security, optimize the encryption-decryption process, and ensure the integrity and confidentiality of information throughout transmission and storage.