Good question when you transform a vector based on

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Good question. When you transform a vector based on beta to a vector based on gama, you are doing a change of basis. 15. We treat transformations just a vector space when concerned about vector addition scalar multiplications. Good point. 16. What is the purpose of A=[T]? Good question. Linear transformation is a very abstract concept, while a matrix is much easier to deal with. 17. Why we always use vectors as rows rather than column vectors?
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Good question. Usually vectors are column vectors. But sometimes, we use row vectors to save space if they don’t cause complications. 18. Is finding [x]_beta similar to finding the span? It is the same as finding the linear combination of x expressed by a set. 19. Why do the polynomials in math 2J/3A and math 121A represent different things? They are notations by different authors. You can create your own notations. 20. What are some applications of linear algebra in real life? Simeple problems like: calculating currents in an electrical circuit; Numerical examples like: least square approximation (linear regression); Complicated problems exist in almost all problems of solving differential equations. 21. Is any basis a span? Yes. 22. We mostly check for linearly independence/dependence and skip the proof of span. Good point. Once we know that the dimension is n, and the set contains n vectors, we only need to check linearly independence OR span. And linearly independence is usually easier to check. If we don’t know the dimension, we need to check both linearly independence and span. 23. What is the difference between span & spanning? I think the difference is: one is a noun, the other is an adjective. If the span of S is V, then S is said to be a spanning set of V. 24. How do you form a basis?
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