WildLinAlg5a: Change of coordinates and determinants
This is the first video of the 5th lecture of this course on Linear Algebra. We analyse the fundamental problem of inverting a change of coordinates, and give applications to solving a system of two linear equations in two unknown. This problem has two interpretations, one in terms of meets of lines, and one in terms of combining vectors to form a given vector. We introduce vectors and matrices in a purely algebraic way. Composing two changes of variable leads to the basic multiplication formula for matrices. This has a close connection with determinants.
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