For first-time learners of linear algebra, several textbooks are recommended based on varying backgrounds and goals. "Elementary Linear Algebra" by Paul Shields is suggested for beginners due to its accessible approach. For mathematics students, "Linear Algebra Done Wrong" by Treil is favored for its comprehensive coverage and free availability. "Introduction to Linear Algebra" by Lang is praised for its clear explanations and smooth transition from analytical geometry to linear algebra. For those interested in applications or engineering, "Linear Algebra and Its Applications" by Lay is highlighted as a top choice. It's advised to review the books personally before making a purchase to ensure the best fit for individual learning styles.