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The problem is asking to find the matrix represented by the expression \((A + B)^T + C\), where the matrices \(A\), \(B\), and \(C\) are given as:

\[
A = \begin{pmatrix} -2 & 3 \\ 3 & 0 \\ 2 & 4 \end{pmatrix}, \quad B = \begin{pmatrix} 4 & 8 \\ 3 & 2 \\ -1 & 0 \end{pmatrix}, \quad C = \begin{pmatrix} 2 & -5 & 6 \\ 3 & 2 & -1 \end{pmatrix}
\]

Let's solve this step by step.

### Step 1: Matrix Addition \(A + B\)

Add the corresponding elements of matrices \(A\) and \(B\):

\[
A + B = \begin{pmatrix} -2+4 & 3+8 \\ 3+3 & 0+2 \\ 2-1 & 4+0 \end{pmatrix} = \begin{pmatrix} 2 & 11 \\ 6 & 2 \\ 1 & 4 \end{pmatrix}
\]

### Step 2: Transpose of \(A + B\)

Now, we take the transpose of the resulting matrix:

\[
(A + B)^T = \begin{pmatrix} 2 & 6 & 1 \\ 11 & 2 & 4 \end{pmatrix}
\]

### Step 3: Add the Matrix \(C\)

Now, add matrix \(C\) to \((A + B)^T\):

\[
(A + B)^T + C = \begin{pmatrix} 2 & 6 & 1 \\ 11 & 2 & 4 \end{pmatrix} + \begin{pmatrix} 2 & -5 & 6 \\ 3 & 2 & -1 \end{pmatrix} = \begin{pmatrix} 4 & 1 & 7 \\ 14 & 4 & 3 \end{pmatrix}
\]

### Final Result:

The matrix representing \((A + B)^T + C\) is:

\[
\boxed{\begin{pmatrix} 4 & 1 & 7 \\ 14 & 4 & 3 \end{pmatrix}}
\]

The correct answer is **option c** in the given choices.

Would you like further details or have any questions?

### Related Questions:
1. How do you calculate the inverse of a matrix?
2. What is the determinant of a 3x3 matrix, and how is it calculated?
3. Can you explain matrix multiplication and its properties?
4. What is the significance of matrix transposition in linear algebra?
5. How can matrix addition and multiplication be used in solving systems of equations?

### Tip: 
Always verify matrix dimensions before adding or multiplying them to avoid dimensional mismatches.

Diketahui matriks A = \begin{pmatrix} -2 & 3 \\ 3 & 0 \\ 2 & 4 \end{pmatrix}, B = \begin{pmatrix} 4 & 8 \\ 3 & 2 \\ -1 & 0 \end{pmatrix}, dan C = \begin{pmatrix} 2 & -5 & 6 \\ 3 & 2 & -1 \end{pmatrix}. Tentukan matriks yang diwakili oleh (A + B)^T + C.

Solve the matrix operation involving addition, transpose, and final addition with another matrix. This problem walks through the steps of adding matrices, taking their transpose, and performing another matrix addition.

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