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.