Low-Rank Adaptation (LoRA) provides a resource-efficient method for fine-tuning large language models, addressing significant computational challenges. Implementing LoRA in the Mistral Large model significantly enhances its performance across a range of complex tasks. The evaluation conducted on the BIG-Bench dataset reveals substantial improvements in accuracy, precision, recall, and perplexity, highlighting the effectiveness of LoRA in optimizing large language models. By focusing on low-rank approximations, LoRA reduces the computational burden of fine-tuning, enabling efficient adaptation without compromising performance. The empirical results demonstrate that the LoRA-adapted model excels in mathematical problem-solving, creative text generation, and common sense reasoning, making it a practical and scalable solution for diverse AI applications. Additionally, the integration of LoRA facilitates seamless implementation with existing transformer architectures, ensuring compatibility and efficiency. The study emphasizes the transformative potential of LoRA to drive significant advancements in natural language processing, providing a resource-efficient method for model adaptation that ultimately enhances the capabilities and applicability of AI systems across various domains. By addressing the challenges of computational resources and adaptation efficiency, LoRA paves the way for more robust and versatile applications of large language models in real-world scenarios.