1.7.i Linear transformations
condition: Let \( \widehat{\mathrm{A}} x=\left(x_{2}-x_{3}, x_{1}, x_{1}+x_{3}\right) \), \( \widehat{\mathrm{B}} x=\left(x_{2}, 2 x_{3}, x_{1}\right) \) linear operators in the space \( \mathbb{R}^{3} \). Find: \( \left(\widehat{\mathrm{A}}+\widehat{\mathrm{B}}^{2}\right) x \).
Linear transformations of matrices in the transition between bases, coordinates of vectors and linear operators.