1.4.19 Matrix transformations

Let the linear operator ( widehat{A} ​​) in the space ( mathbb{V}_{3} ) of geometric vectors be determined by the action of the mapping ( alpha ) to the ends of the radius vectors of points in three-dimensional space. Let A be the matrix of the operator ( widehat{A} ​​) in the canonical basis ( i, j, k ). Find the eigenvalues ​​and eigenvectors of matrix A. Explain how the result is related to the geometric action of the operator ( widehat{A} ​​). The mapping ( alpha ) is a projection onto the plane ( x+y+z=0 ).