The image contains some linear algebra problems involving matrices. Let's break down the key questions and solve them:

1. Question 7 asks about the inverse of a matrix:

   • The given matrix $D$ is: 0 & 0 \\ 0 & 2024 \end{pmatrix}$$
   • For a matrix to have an inverse, its determinant must be non-zero. The determinant of matrix $D$ is $0 \times 2024 - 0 \times 0 = 0$. Since the determinant is zero, matrix $D$ is singular, meaning it does not have an inverse.

2. Question 8 involves solving a system of linear equations using matrix representation:

   • The matrix system is given as: 1 & 2 & -1 \\ 2 & -1 & 1 \\ -1 & 1 & 1 \\ \end{pmatrix} \begin{pmatrix} x \\ y \\ z \\ \end{pmatrix} = \begin{pmatrix} 4 \\ 0 \\ 1 \\ \end{pmatrix}$$
   • To solve this, we can use methods like Gaussian elimination or matrix inversion if the coefficient matrix is invertible.
   • Calculating the determinant of the coefficient matrix: [ \text{det} = 1(-1 \cdot 1 -