Question 8 - Week 7 Practice

Passage

Consider a linear transformation

T:\mathbb{R}^3\to\mathbb{R}^3

defined as

T(x,y,z)=(x+2y,\ 2x-y+\alpha z,\ 3x+y+\beta z)

, where

\alpha,\beta\in\mathbb{R}

. Let

A

be the matrix representation of

T

with respect to the standard bases for both the domain and codomain. Suppose

A

is similar to

B=\begin{bmatrix}1&2&3\\4&-5&-6\\-5&3&3\end{bmatrix}.

Based on the above information, answer the given subquestions.

Question

Choose all the correct statements.

Passage question