PassageConsider a linear transformation T:R3→R3T:\mathbb{R}^3\to\mathbb{R}^3 defined as T(x,y,z)=(x+2y, 2x−y+αz, 3x+y+βz)T(x,y,z)=(x+2y,\ 2x-y+\alpha z,\ 3x+y+\beta z), where α,β∈R\alpha,\beta\in\mathbb{R}. Let AA be the matrix representation of TT with respect to the standard bases for both the domain and codomain. Suppose AA is similar to B=[1234−5−6−533].B=\begin{bmatrix}1&2&3\\4&-5&-6\\-5&3&3\end{bmatrix}. Based on the above information, answer the given subquestions.
