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x, y, z be (non-zero) vectors and suppose that z = -2x + 2y and w = -6x + 6y - 1z. Are the following statements true or false? Span(w, x) = Span(x, y) Span(w, y) = Span(w, y, z) Span(w, z) = Span(x, z)

x, y, z be (non-zero) vectors and suppose that z = -2x + 2y and w = -6x + 6y - 1z. Are the following statements true or false? Span(w, x) = Span(x, y) Span(w, y) = Span(w, y, z) Span(w, z) = Span(x, z)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.3: Lines And Planes
Problem 18EQ
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Problem 11. Let x, y, z be (non-zero) vectors and suppose that z = −2x + 2y and w = −6x + 6y – 1z. Are the following statements true or false? 1. Span(w, x) = Span(x, y) ? ? ? ? ? 2. Span(w, y) = Span(w, y, z) 3. Span(w, z) = Span(x, z) 4. Span(w, x, y) = Span(x, z) Span(w, x) = Span(w, z)
Transcribed Image Text:Problem 11. Let x, y, z be (non-zero) vectors and suppose that z = −2x + 2y and w = −6x + 6y – 1z. Are the following statements true or false? 1. Span(w, x) = Span(x, y) ? ? ? ? ? 2. Span(w, y) = Span(w, y, z) 3. Span(w, z) = Span(x, z) 4. Span(w, x, y) = Span(x, z) Span(w, x) = Span(w, z)
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