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Euclidean Spaces and Subspaces

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1. Let W = {(a, b ,2a - 3b, -a + 2b)} whre a and b are real numbers.
(a) In what Euclidean space does this subset reside? Explain your answer.
(b) Show that W is a subspace by showing that it satisfies the closure properties.
(c) Show that W is a subspace by describing W as the span of a set of vectors.
(d) Explain why this subspace is a plane.

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Solution Summary

Euclidean Spaces and Subspaces are investigated. The expert determines in what Euclidean space does a subset reside in.

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(a) W consists of 4-tuples of real numbers, so W is a subset of R^4.

(b) We need to check that W is closed under addition of vectors and under scalar mutliplication (by real ...

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