Chapter 3.4, Problem 36E

Let $=\left({\stackrel{\to }{v}}_1,{\stackrel{\to }{v}}_2,{\stackrel{\to }{v}}_3\right)$be any basis of ${ℝ}^3$consisting of perpendicular unit vectors, such that ${\stackrel{\to }{v}}_3={\stackrel{\to }{v}}_1\times {\stackrel{\to }{v}}_2$ . In Exercises 31 through 36, find the matrix B of the given linear transformation T from ${ℝ}^3$to ${ℝ}^3$. Interpret T geometrically.

36. $T\left(\stackrel{\to }{x}\right)={\stackrel{\to }{v}}_1\times \stackrel{\to }{x}+\left({\stackrel{\to }{v}}_1\cdot \stackrel{\to }{x}\right){\stackrel{\to }{v}}_1$