The ubiquitous nature of technology has undoubtedly reshaped our lives, including the educational sector where it has broken down geographical barriers and transcended traditional means of acquiring knowledge. Online tutoring, a byproduct of such advancements, is revolutionizing the way we learn complex subjects like Linear Algebra. Despite its abstract nature, Linear Algebra has practical applications in diverse fields such as computer science, physics, and economics. However, the subject's intricate and multidimensional concepts often require personalized guidance for a thorough understanding. This is where the role of an online Linear Algebra tutor comes in. Thus, here are six compelling reasons that argue the necessity of an online linear algebra tutor.

The first reason is the flexibility and convenience that online tutoring offers. Traditional in-person tutoring is bound by the constraints of time and location. An online tutor, on the other hand, is accessible at your preferred time and place, providing you with the luxury to learn at your own pace. Moreover, this flexibility is particularly beneficial for those juggling multiple commitments such as work, family, and other academic pursuits.

Secondly, an online Linear Algebra tutor provides customized and personalized learning experiences. Every student has unique learning needs and styles, and a generic approach to teaching might not cater to these individual requirements. Online tutors can modify teaching methods and pace according to the student's aptitude, thereby leading to a deeper understanding of the subject.

The third reason concerns the technological tools that online tutors can leverage to enhance the learning process. Utilizing interactive whiteboards, video conferencing, and real-time document editing, the tutor can create engaging visualizations and demonstrations. These tools are especially useful for a subject like Linear Algebra, where visual representation of abstract concepts can significantly aid comprehension.

Fourth, online tutoring provides a safe learning environment with less pressure and intimidation, which sometimes characterize traditional classrooms. In an online setting, students might feel more comfortable asking questions, expressing their doubts, and making mistakes. This freedom fosters an open dialogue between the student and the tutor, leading to a more productive learning experience.

Fifth, the efficacy of online tutoring is backed by research. A comprehensive study by the U.S. Department of Education concluded that students who pursued online learning performed better, on average, than those receiving face-to-face instruction.

Finally, online tutoring is cost-effective. It eliminates transportation costs and time associated with traditional tutoring. Moreover, the competitive online market of tutors ensures reasonable pricing without compromising the quality of instruction.

However, like any technology, online tutoring is not without its trade-offs. Despite its numerous benefits, the lack of physical presence may create a disconnect, and technical issues might disrupt the learning process. But, with steady technological advancements and effective communication, these challenges can be mitigated.

It’s speculation to say that the future of education resides solely in the digital realm, but what is irrefutable is that online learning is a powerful tool that has democratized education. The advantages of an online Linear Algebra tutor are manifold - flexibility, personalization, innovative teaching tools, a comfortable learning environment, empirical support, and cost-effectiveness. These compelling reasons are enough to affirm the indispensability of an online Linear Algebra tutor in mastering this complex yet fascinating subject.