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We are given two matrices \( A \) and \( B \) as follows:

\[
A = \begin{bmatrix} 2 & -1 \\ 4 & 2 \end{bmatrix}, \quad B = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}
\]

We need to compute \( A - B \) and \( A + B \).

### 1. Matrix subtraction \( A - B \):
\[
A - B = \begin{bmatrix} 2 & -1 \\ 4 & 2 \end{bmatrix} - \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}
\]
Subtracting corresponding elements:
\[
A - B = \begin{bmatrix} 2 - 2 & -1 - 3 \\ 4 - 1 & 2 - 2 \end{bmatrix} = \begin{bmatrix} 0 & -4 \\ 3 & 0 \end{bmatrix}
\]

### 2. Matrix addition \( A + B \):
\[
A + B = \begin{bmatrix} 2 & -1 \\ 4 & 2 \end{bmatrix} + \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}
\]
Adding corresponding elements:
\[
A + B = \begin{bmatrix} 2 + 2 & -1 + 3 \\ 4 + 1 & 2 + 2 \end{bmatrix} = \begin{bmatrix} 4 & 2 \\ 5 & 4 \end{bmatrix}
\]

### Final Results:
\[
A - B = \begin{bmatrix} 0 & -4 \\ 3 & 0 \end{bmatrix}, \quad A + B = \begin{bmatrix} 4 & 2 \\ 5 & 4 \end{bmatrix}
\]

Would you like further details or clarifications?

### Related Questions:
1. How do you multiply two matrices together?
2. What is the determinant of matrix \( A \) or \( B \)?
3. How do you calculate the inverse of a 2x2 matrix?
4. What are the eigenvalues of matrix \( A \) or \( B \)?
5. How is matrix addition and subtraction used in solving linear systems?

### Tip:
When adding or subtracting matrices, make sure they are of the same dimensions; otherwise, the operation is not defined.

If A = [[2, -1], [4, 2]] and B = [[2, 3], [1, 2]], compute A - B and A + B.

Learn how to perform matrix addition and subtraction with the 2x2 matrices A = [[2, -1], [4, 2]] and B = [[2, 3], [1, 2]]. This problem demonstrates key linear algebra concepts and is suitable for students in Grades 9-12.

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