Determine which of the following subsets of R³ are subspaces. Briefly explain. i) The set S1 of vectors (x, y, z) E R³ such that xyz = 0 ii) The set S2 of vectors (x, y, z) E R³ such that x + y + z = 0 iii) The set S1 of vectors (x, y, z) E R³ such that y? + z² = 0 iv) The set S1 of vectors (x, y, z) E R³ such that y² – 2² = 0

Determine which of the following subsets of R³ are subspaces. Briefly explain. i) The set S1 of vectors (x, y, z) E R³ such that xyz = 0 ii) The set S2 of vectors (x, y, z) E R³ such that x + y + z = 0 iii) The set S1 of vectors (x, y, z) E R³ such that y? + z² = 0 iv) The set S1 of vectors (x, y, z) E R³ such that y² – 2² = 0

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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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Determine which of the following subsets of R³ are subspaces. Briefly explain.
i) The set S1 of vectors (x, y, z) E R³ such that xyz = 0
ii) The set S2 of vectors (x, y, z) E R³ such that x + y + z = 0
iii) The set S1 of vectors (x, y, z) E R³ such that y? + 22 = 0
iv) The set S1 of vectors (x, y, z) E R³ such that y? – z2 = 0

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