Question: User: That's incorrect. Let $x$ be the given matrix. Write $x$ in terms of $e_1$ and $e_2$. Then, find $T(x)$ using the resulting expression. Finally, write $T(x)$ in terms of $y_1$ and $y_2$ and then simplify.

1. **State the problem:** We are given a matrix $x$ and need to express it in terms of basis vectors $e_1$ and $e_2$. 2. **Express $x$ in terms of $e_1$ and $e_2$:** Suppose $x = a e_1 + b e_2$ where $a$ and $b$ are scalars to be determined. 3. **Find $T(x)$ using linearity:** Since $T$ is linear, $T(x) = T(a e_1 + b e_2) = a T(e_1) + b T(e_2)$. 4. **Write $T(x)$ in terms of $y_1$ and $y_2$:** Assume $T(e_1) = y_1$ and $T(e_2) = y_2$, so $T(x) = a y_1 + b y_2$. 5. **Simplify the expression:** Combine like terms or simplify coefficients if possible. **Note:** Without explicit matrices or vectors for $x$, $e_1$, $e_2$, $y_1$, and $y_2$, this is the general method to solve the problem. If you provide the specific matrices or vectors, I can compute the exact values for $a$, $b$, and the simplified form of $T(x)$.