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HConsider the vector space R° (over R) and ZcR consisting of vectors z=(z1, z2 z3), with these properties: (a) (b) z,+Z,=0 (c) Z,=0 z,+z2=1 In which of these cases is Z a subspace?

HConsider the vector space R° (over R) and ZcR consisting of vectors z=(z1, z2 z3), with these properties: (a) (b) z,+Z,=0 (c) Z,=0 z,+z2=1 In which of these cases is Z a subspace?

Advanced Engineering Mathematics
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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**Problem 8: Vector Spaces and Subspaces** Consider the vector space \(\mathbb{R}^3\) (over \(\mathbb{R}\)) and let \(Z \subseteq \mathbb{R}^3\) consist of vectors \(\vec{z} = (z_1, z_2, z_3)\) with the following properties: (a) \(z_1 = 0\) (b) \(z_1 + z_2 = 0\) (c) \(z_1 + z_2 = 1\) In which of these cases is \(Z\) a subspace?
Transcribed Image Text:**Problem 8: Vector Spaces and Subspaces** Consider the vector space \(\mathbb{R}^3\) (over \(\mathbb{R}\)) and let \(Z \subseteq \mathbb{R}^3\) consist of vectors \(\vec{z} = (z_1, z_2, z_3)\) with the following properties: (a) \(z_1 = 0\) (b) \(z_1 + z_2 = 0\) (c) \(z_1 + z_2 = 1\) In which of these cases is \(Z\) a subspace?
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Given Z⊂R3, where R3 vector space.z→=(z1,z2,z3)(a) z1=0(b) z1+z2=0(c) z1+z2=1We have to check in which of the cases is Z a subspace?

 

 

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