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.

2 Consider the matrix A = and the vector u = Let B = (A – A")2 and define vector v = Bu. If v = , write 1 down the value of vị. [Please enter your answer numerically in decimal format.

If A = [a1, a2, a3] has as columns the three vectors a1, a2, and a3. What is y = Ax,where x is a vector with three components, x1, x2, x3? Is y in the column spaceof A?

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