1.7.18 Linear transformations

condition: In the basis in which the subspace equations are written, find the linear transformation matrix \( \varphi \) of a three-dimensional geometric vector space, indicate the eigenvalues ​​and eigenvectors of the transformation, describe its kernel and image, if \( \varphi \) exists: symmetry with respect to the plane \( x-2 y-2 z=0 \) parallel to the line \( x=2 t \), \( y=t, z=3 t \)