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To find \(A - B\) and \(A + B\), we will subtract and add the corresponding elements of matrices \(A\) and \(B\).

Given:
\[ A = \begin{pmatrix}
1 & 0 & 1 & 2 \\
0 & -1 & -2 & 3 \\
4 & -3 & 1 & 5 \\
2 & -4 & -1 & 0
\end{pmatrix} \]
\[ B = \begin{pmatrix}
5 & 3 & -1 & 8 \\
2 & 0 & 7 & 4 \\
-2 & -3 & -3 & -5 \\
4 & 1 & 1 & -2
\end{pmatrix} \]

### Finding \(A - B\):
\[ A - B = \begin{pmatrix}
1-5 & 0-3 & 1-(-1) & 2-8 \\
0-2 & -1-0 & -2-7 & 3-4 \\
4-(-2) & -3-(-3) & 1-(-3) & 5-(-5) \\
2-4 & -4-1 & -1-1 & 0-(-2)
\end{pmatrix} \]
\[ A - B = \begin{pmatrix}
-4 & -3 & 2 & -6 \\
-2 & -1 & -9 & -1 \\
6 & 0 & 4 & 10 \\
-2 & -5 & -2 & 2
\end{pmatrix} \]

### Finding \(A + B\):
\[ A + B = \begin{pmatrix}
1+5 & 0+3 & 1+(-1) & 2+8 \\
0+2 & -1+0 & -2+7 & 3+4 \\
4+(-2) & -3+(-3) & 1+(-3) & 5+(-5) \\
2+4 & -4+1 & -1+1 & 0+(-2)
\end{pmatrix} \]
\[ A + B = \begin{pmatrix}
6 & 3 & 0 & 10 \\
2 & -1 & 5 & 7 \\
2 & -6 & -2 & 0 \\
6 & -3 & 0 & -2
\end{pmatrix} \]

So, the matrices \(A - B\) and \(A + B\) are:

\[ A - B = \begin{pmatrix}
-4 & -3 & 2 & -6 \\
-2 & -1 & -9 & -1 \\
6 & 0 & 4 & 10 \\
-2 & -5 & -2 & 2
\end{pmatrix} \]
\[ A + B = \begin{pmatrix}
6 & 3 & 0 & 10 \\
2 & -1 & 5 & 7 \\
2 & -6 & -2 & 0 \\
6 & -3 & 0 & -2
\end{pmatrix} \]

Would you like more details or have any questions?

Here are five questions you can ask:
1. How do you determine the determinant of a matrix?
2. Can you explain matrix multiplication with examples?
3. What is the inverse of a matrix, and how is it computed?
4. How do you solve a system of linear equations using matrices?
5. What are eigenvalues and eigenvectors of a matrix?

**Tip:** When performing matrix operations, always ensure the matrices are of compatible dimensions. For addition and subtraction, both matrices must have the same dimensions.

Learn how to find matrices A - B and A + B using matrix addition and subtraction with a step-by-step solution. This problem covers matrix operations, suitable for advanced high school students.

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