The labyrinth of linear algebra often calls for professional guidance to navigate its complex landscapes, and the digital age proffers a vast array of platforms that offer these services. The choice, however, can often be overwhelming, and hence it becomes crucial to discern the criteria for selecting an online linear algebra tutor, who can best cater to your unique needs - a task that is often more challenging than the subject itself. In the spirit of efficient decision-making, this article proposes pertinent questions one should pose in this pursuit, which not only cover the essential aspects of the tutoring process but also factor in the latest developments in the field, technology, and pedagogy.

Linear algebra, an integral branch of mathematics, involves the study of vectors, vector spaces (also known as linear spaces), linear transformations, and systems of linear equations. It finds applications in various fields such as physics, engineering, computer science, economics, and statistics. Given this universal applicability, an understanding of linear algebra becomes imperative. The traditional classroom learning process, however, may not always cater to the diverse learning styles and pace of individuals. This is where online tutors bridge the gap, offering personalized, flexible, and accessible learning solutions.

Begin your selection process by inquiring about the prospective tutor's educational qualifications and professional experience. While a degree in mathematics or a related field is a basic requirement, additional certifications in teaching or tutoring can add a layer of credibility. Furthermore, their professional experience, particularly in teaching linear algebra, can be a testament to their expertise.

Next, ask about their familiarity with and use of technology. Given this tutoring occurs in an online environment, the tutor's adeptness with digital tools is crucial. This could range from using interactive whiteboards and shared documents to utilizing advanced mathematical software to illustrate complex concepts. An ability to adapt to various teaching platforms also becomes necessary, especially if you have a preferred platform of use.

Additionally, probe their teaching methodology. Linear algebra, with its abstract concepts and myriad theorems, requires an understanding of fundamental principles rather than rote memorization. Hence, tutors who adopt an inquiry-based learning approach, encouraging students to actively construct their knowledge, tend to be more effective. They should also be capable of contextualizing the concepts, linking linear algebra to real-world applications, making the learning process more engaging and meaningful.

Furthermore, ask about their strategies for assessing and providing feedback on your progress. Regular formative assessments, which involve consistent feedback and guidance, are critical for improvement. The tutor should be able to provide a comprehensive evaluation of your strengths and weaknesses and tailor their teaching accordingly.

Finally, discuss their availability and flexibility. The convenience of online tutoring can be nullified if the tutor’s schedule doesn’t align with yours. Hence, a tutor who can accommodate your time zones and other commitments would be ideal.

Cost is often a deciding factor for many, and while it is important, it should not be the only determinant. A higher-priced tutor with the right expertise and approach can provide a better return on investment than a cheaper, less experienced one.

The decision ultimately boils down to a balance of various factors - the tutor's qualifications, teaching approach, technological prowess, and scheduling flexibility. By asking these questions, you equip yourself with the necessary information to make an informed choice. Remember, the goal is to find a tutor who understands your learning needs and can guide you effectively through the realm of linear algebra.

Selecting an online tutor is a strategic investment in your education. Therefore, exercise due diligence in this selection process, just as one would when making a significant financial investment. After all, the dividends of a good education are immeasurable.