1.7.23 Linear Transformations

Condition: Given linear operators \ (\ varphi \) and \ (\ psi \) in space \ (v^{3} \). 1. Find the matrices of operators \ (\ varphi, \ psi \) and \ (\ varphi \ cdot \ psi \) in the basis \ (i, j, k \). 2. Find the nucleus and image of operators \ (\ varphi \) and \ (\ psi \). In the case of a nonsense, describe their equations. 3. Find out if there is a reverse operator for \ (\ varphi \ cdot \ psi \). If so, then describe its geometric meaning; If not, then indicate the reason. \ (\ varphi \)-the turn around the axis \ (o z \) on \ (90^{\ circ}, \ psi \)-orthogonal design on the plane \ (x-y+z = 0 \).