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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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    (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 ...

    Solution Summary

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