This video explains how to find the standard basis coordinates of a vector given a nonstandard basis and nonstandard coordinates.
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(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
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Understanding alternate coordinate systems
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/change_of_basis/v/linear-algebra-change-of-basis-matrix?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
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Find the coordinate vector of x with respect to the basis B. This is a confusing question at first but should be fairly simple to evaluate.
