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The image contains a matrix algebra problem. Here's a transcription of the problem:

**Given:**
\[
A = \begin{bmatrix} 4 & 2 \\ 1 & 5 \end{bmatrix}, \quad B = \begin{bmatrix} 1 & 2 \\ -3 & 4 \end{bmatrix}, \quad C = \begin{bmatrix} -2 & 1 & 3 \\ 5 & 4 & 2 \end{bmatrix}
\]

**Determine:**
1. \( (3A - B) + 2A \)
2. \( 5A - (BA) \)
3. \( (AB)^T C \)
4. \( C^T B \)
5. \( (2A)C - BC \)

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Given the matrices A, B, and C, determine the following expressions: (3A - B) + 2A, 5A - (BA), (AB)^T C, C^T B, (2A)C - BC.

Explore how to solve complex matrix algebra expressions involving multiplication, transposition, and addition. This guide provides a detailed step-by-step solution for determining (3A - B) + 2A, 5A - (BA), (AB)^T C, C^T B, and (2A)C - BC, suitable for advanced high school and undergraduate students.

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