Find A + A^T

Given:

\[ A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \]

Step 1: Find A^T

\[ A^T = \begin{bmatrix} 1 & 3 \\ 2 & 4 \end{bmatrix} \]

Step 2: Add Matrices

\[ A + A^T = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} + \begin{bmatrix} 1 & 3 \\ 2 & 4 \end{bmatrix} = \begin{bmatrix} 2 & 5 \\ 5 & 8 \end{bmatrix} \]

Final Answer:

\[ A + A^T = \begin{bmatrix} 2 & 5 \\ 5 & 8 \end{bmatrix} \]