**Vectors and Span in 3D Space**Let \(\vec{v}_1, \vec{v}_2, \vec{v}_3\) be any vectors in a 3-dimensional space. Determine whether the following statements are true or false. You do not have to justify your answer:1. \(\text{span}(\vec{v}_1, \vec{v}_2, \vec{v}_3) = \text{span}(3\vec{v}_2, -\vec{v}_3, \vec{v}_1)\)2. \(\text{span}(\vec{v}_1, \vec{v}_2, \vec{v}_3) = \text{span}(\vec{v}_1 + \vec{v}_2, \vec{v}_2 - \vec{v}_1, \vec{v}_3)\)3. If \(\text{span}(\vec{v}_1, \vec{v}_2) = \text{span}(\vec{v}_1, \vec{v}_3)\), then \(\vec{v}_2\) and \(\vec{v}_3\) are parallel.4. If \(\vec{v}_1\) is a linear combination of \(\vec{v}_2\) and \(\vec{v}_3\), then \(\text{span}(\vec{v}_1, \vec{v}_2, \vec{v}_3) = \text{span}(\vec{v}_2, \vec{v}_3)\).5. If \(\vec{v}_3\) is not a linear combination of \(\vec{v}_1\) and \(\vec{v}_2\), then \(\text{span}(\vec{v}_1, \vec{v}_2, \vec{v}_3)\) is strictly larger than \(\text{span}(\vec{v}_1, \vec{v}_2)\).

Let 71, 72, 73 be any vectors in a 3-dimensional space. Determine whether the following statements are true or false. You do not have to justify your answer: span(1, U2, U3) = span(302, U3, U1) span(V1, V2, V3) span(v₁ + √2, V2 - V1, V3) If span(7₁, 7₂) = span(7₁, 73), then 72 and 73 are parallel. If 7 = → →

Let 71, 72, 73 be any vectors in a 3-dimensional space. Determine whether the following statements are true or false. You do not have to justify your answer: span(1, U2, U3) = span(302, U3, U1) span(V1, V2, V3) span(v₁ + √2, V2 - V1, V3) If span(7₁, 7₂) = span(7₁, 73), then 72 and 73 are parallel. If 7 = → →

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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