MHB How Can Basis Vectors Simplify Real-World Problems?

matqkks
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What is attractive way to introduce basis vectors? I am looking for a hook that students will find motivating. It needs to have an impact. I have normally introduced it by just stating independent vectors that span the space.
 
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I've never taught linear algebra, but selecting a basis is essentially selecting a coordinate system, which allows identifying each point (vector) with a unique sequence of numbers. Coordinate systems are obviously crucial for solving many practical problems.
 

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