1.7.11 Linear Transformations

Condition: linear operator \ (\ widehat {a} \) in the space \ (\ mathbb {v} _ {3} \) geometric vectors is determined by the effect of display \ (\ alpha \) on the ends of the radius by the points of the three-dimensional space. 1) Find the matrix of the linear operator \ (\ widehat {a} \) in the suitable basis of space \ (\ mathbb {v} _ {3} \), and then in the canonical basis \ (i, j, k \). 2) at what point of the three -dimensional space does the point with the coordinates \ ((1,0,0) \) under the influence of display \ (\ alpha \)? 3) Find \ (a^{n} \), where \ (A \) is the operator matrix in the basis \ (i, j, k \). Display \ (\ alpha \)-design on the plane \ (x+y+z = 0 \).