1.7.16 Linear transformations

condition: The linear operator \( \hat{C} \) in the space \( \mathbb{V}_{3} \) is a sequential application of the linear operators \( \widehat{A} ​​\) and \( \widehat{\mathrm{B}} \). Find the operator matrices \( \widehat{\mathrm{A}}, \widehat{\mathrm{B}}, \widehat{\mathrm{C}} \) in the basis \( i, j, k \). Is the operator \( \hat{C} \) invertible? If yes, then describe its geometric action. Operator \( \widehat{\mathrm{A}} \) - reflection relative to the plane \( X O Y \), Operator \( \widehat{B} \) - homothety with coefficient \( k=2 \)