1.4.19 Matrix Transformations

Let the linear operator (widehat {a}) in the space (mathbb {v} _ {3}) of geometric vectors are determined by the effect of display (alpha) on the ends of the radius of the points of the three -dimensional space. Let A - the matrix of the operator (widehat {a}) in the canonical basis (i, j, k). Find your own values ​​and own vectors of the matrix A. Explain how the result is related to the geometric effect of the operator (widehat {a}). Display (Alpha) is designing on the plane (X+Y+Z = 0).