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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:
     \[
     D = \begin{pmatrix}
     0 & 0 \\
     0 & 2024
     \end{pmatrix}
     \]
   - 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:
     \[
     \begin{pmatrix}
     1 & 2 & -1 \\
     2 & -1 & 1 \\
     -1 & 1 & 1 \\
     \end{pmatrix}
     \begin{pmatrix}
     x \\
     y \\
     z \\
     \end{pmatrix}
     =
     \begin{pmatrix}
     4 \\
     0 \\
     1 \\
     \end{pmatrix}
     \]
   - 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 -

The image contains a set of linear algebra problems involving matrices, including matrix inversion and solving systems of linear equations.

Learn how to solve matrix-related problems, including finding the inverse of a matrix and solving systems of linear equations. This example includes matrix determinant calculations and matrix multiplication. Ideal for students studying Linear Algebra at the college level.

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