First Sentence:
There are two ways to motivate the notion of a vector: one is by means of lists of numbers and subscripts, and the other is by means of certain objects in physics.
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Key Phrases - Statistically Improbable Phrases (SIPs):
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distinct linear polynomials, using unknown scalars, row canonical form, elementary matrix corresponding, following symmetric matrices, find formulas defining, diagonal matrix relative, one independent solution, find the coordinate vector, set corresponding entries, square block matrix, same row space, pivot variables, echelon matrix, following linear maps, corresponding column operation, echelon matrices, two nonzero rows, primary decomposition theorem, preceding vectors, echelon form, row equivalence, diagonal matrix representation, pivot entry, find the characteristic polynomial
Key Phrases - Capitalized Phrases (CAPs):
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Prove Theorem, Supplementary Problems, Solved Problems, Forward Elimination, Repeat Problem, Prove Lemma, Apply Algorithm, Backward Elimination, Linear Property, Repeat Step, Suppose Jul
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