Euclidean Spaces and Subspaces
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.
https://brainmass.com/math/vector-calculus/euclidean-spaces-subspaces-126540
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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.
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