The image shows a linear algebra problem. You are given the matrix $A$ and the vector $b$ as:

$A = \begin{pmatrix} -4 & 2 & -5 \\ 3 & -4 & 0 \\ -5 & 3 & -4 \end{pmatrix}, \quad b = \begin{pmatrix} -13 \\ -21 \\ -126 \end{pmatrix}$

The task is to find a vector $x$ such that:

$T(x) = A x = b$

This involves solving the system of linear equations $A x = b$. Let me solve this system and find the vector $x$.The solution to the system $A x = b$ is the vector:

$x = \begin{pmatrix} 163.93 \\ 128.20 \\ -77.27 \end{pmatrix}$

This is the vector $x$ whose image under the transformation $T(x) = A x$ is the given vector $b$.

Would you like more details or have any other questions?

Here are five related questions you might find interesting:

1. How can we verify that $A x = b$ holds true?
2. What is the determinant of matrix $A$?
3. What is the rank of the matrix $A$?
4. Can this system of equations be solved using Gaussian elimination?
5. How would you interpret the linear transformation geometrically?

Tip: Always check if a matrix is invertible before solving a system of equations, as it guarantees a unique solution.