Chapter 2.1, Problem 44E

The cross product of two vectors in ${ℝ}^3$ is given by
$\left[\begin{array}{l}{a}_1\\ a_2\\ a_3\end{array}\right]\times \left[\begin{array}{l}{b}_1\\ b_2\\ b_3\end{array}\right]=\left[\begin{array}{l}{a}_2{b}_3-a_3{b}_2\\ a_3{b}_1-a_1{b}_3\\ a_1{b}_2-a_2{b}_1\end{array}\right]$ .
See Definition A.9 and Theorem A.11 in theAppendix. Consider an arbitrary vector $\stackrel{\to }{v}$ in ${ℝ}^3$ . Is thetransformation $T\left(\stackrel{\to }{x}\right)=\stackrel{\to }{v}\times \stackrel{\to }{x}$ from ${ℝ}^3$ to ${ℝ}^3$ linear?If so. find its matrix in terms of the components of thevector $\stackrel{\to }{v}$ .