# 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.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.6: Rank Of A Matrix And Systems Of Linear Equations
Problem 69E: Consider an mn matrix A and an np matrix B. Show that the row vectors of AB are in the row space of...
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