Let (a) Show that the solution to the linear system x Ax represents a rotation of R 3 around the z axis What is the trajectory of a point x 0 (b) Show that the solution to the inhomogeneous system x Ax b represents a screw motion of R 3 around the z axis What is the trajectory of a point x 0 (c) More generally, given 0 a R 3 , show that the solution to x a x a represents a family of screw motions along the axis a A 0 1 0 00 1 0 00 b 0 1

Question: Let (a) Show that the solution to the linear system x = Ax represents a rotation of R 3 around the z-axis. What is the

Let A = 0 -1 0 00 1 0 00 b= 0 1

(a) Show that the solution to the linear system ẋ = Ax represents a rotation of R³around the z-axis. What is the trajectory of a point x₀?

(b) Show that the solution to the inhomogeneous system ẋ = Ax + b represents a screw motion of R³around the z-axis. What is the trajectory of a point x₀?

(c) More generally, given 0 ≠ a ∈ R³, show that the solution to ẋ = a × x + a represents a family of screw motions along the axis a.

A = 0 -1 0 00 1 0 00 b= 0 1

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ANSWER a The matrix A can be written as A 0 1 0 1 0 0 0 0 0 Let xt be a solution to x Ax Then we hav... View full answer

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