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The four matrices Sx, Sy, S and I are defined by 0 -1 where i2-1. Show that S I and SS iS,, and obtain similar results by permutting x, y and z. Given that v is a vector with Cartesian components (vx, Dy, Dz), the matrix S(v) is defined as Prove that, for general non-zero vectors a and b, S(a)S(b) a bl+iS(a x b). Without further calculation, deduce that S(a) and S(b) commute if and only if a and b are parallel vectors.

The four matrices Sx, Sy, S and I are defined by 0 -1 where i2-1. Show that S I and SS iS,, and obtain similar results by permutting x, y and z. Given that v is a vector with Cartesian components (vx, Dy, Dz), the matrix S(v) is defined as Prove that, for general non-zero vectors a and b, S(a)S(b) a bl+iS(a x b). Without further calculation, deduce that S(a) and S(b) commute if and only if a and b are parallel vectors.

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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The four matrices Sx, Sy, S and I are defined by 0 -1 where i2-1. Show that S I and SS iS,, and obtain similar results by permutting x, y and z. Given that v is a vector with Cartesian components (vx, Dy, Dz), the matrix S(v) is defined as Prove that, for general non-zero vectors a and b, S(a)S(b) a bl+iS(a x b). Without further calculation, deduce that S(a) and S(b) commute if and only if a and b are parallel vectors.
Transcribed Image Text:The four matrices Sx, Sy, S and I are defined by 0 -1 where i2-1. Show that S I and SS iS,, and obtain similar results by permutting x, y and z. Given that v is a vector with Cartesian components (vx, Dy, Dz), the matrix S(v) is defined as Prove that, for general non-zero vectors a and b, S(a)S(b) a bl+iS(a x b). Without further calculation, deduce that S(a) and S(b) commute if and only if a and b are parallel vectors.
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