The document uploaded appears to be a math practice assignment for a course on "Fundamentals of Architecture and Urbanism" that includes exercises related to linear algebra. Here's a summary of the tasks provided:

1. Calculate the matrix of the endomorphism F in the usual basis.
2. Determine if the set of vectors $\{v_1, v_2, v_3\}$ forms a basis. If not, find an orthogonal space that serves as a basis in $\mathbb{R}^3$.
3. Calculate the coordinates of vector $u = [3, 2a, b]$ in the basis $\{v_1, v_2, v_3\}$, where $a$ and $b$ are the last two digits of your ID number.
4. Find the matrix of F in the basis $\{v_1, v_2, v_3\}$.
5. Check if the endomorphism F is diagonalizable. If it is, determine the characteristic polynomial and the corresponding basis of eigenvectors. Then, provide the matrix representation of the endomorphism in this eigenvector basis.

Would you like me to walk through the solution for any specific part of this assignment?

Here are some related questions to consider:

1. How do you determine if a set of vectors forms a basis in $\mathbb{R}^3$?
2. What is the process for calculating the matrix of an endomorphism in a given basis?
3. How can you check if an endomorphism is diagonalizable?
4. What is the significance of the characteristic polynomial in determining diagonalizability?
5. How do you find the coordinates of a vector in a different basis?

Tip: Remember, a set of vectors forms a basis if they are linearly independent and span the entire vector space. In $\mathbb{R}^3$, you need three linearly independent vectors for a basis.