You've uploaded a problem set containing matrix-related questions. I will help with the first question and provide detailed solutions. The first question asks:

1. Diketahui: $A = \begin{bmatrix} 3 & -4 \\ 2 & 1 \end{bmatrix}, B = \begin{bmatrix} -3 & 5 \\ -2 & 1 \end{bmatrix}, C = \begin{bmatrix} 5 & -2 \\ -4 & -1 \end{bmatrix}$

Find: $3A^T - B + 2C$

Steps to solve:

1. Transpose of A (A^T): $A^T = \begin{bmatrix} 3 & 2 \\ -4 & 1 \end{bmatrix}$

2. Multiply $A^T$ by 3: $3A^T = 3 \times \begin{bmatrix} 3 & 2 \\ -4 & 1 \end{bmatrix} = \begin{bmatrix} 9 & 6 \\ -12 & 3 \end{bmatrix}$

3. Multiply C by 2: $2C = 2 \times \begin{bmatrix} 5 & -2 \\ -4 & -1 \end{bmatrix} = \begin{bmatrix} 10 & -4 \\ -8 & -2 \end{bmatrix}$

4. Now, compute $3A^T - B + 2C$: $B = \begin{bmatrix} -3 & 5 \\ -2 & 1 \end{bmatrix}$

   Perform the subtraction and addition: $3A^T - B = \begin{bmatrix} 9 & 6 \\ -12 & 3 \end{bmatrix} - \begin{bmatrix} -3 & 5 \\ -2 & 1 \end{bmatrix} = \begin{bmatrix} 12 & 1 \\ -10 & 2 \end{bmatrix}$ Then: $3A^T - B + 2C = \begin{bmatrix} 12 & 1 \\ -10 & 2 \end{bmatrix} + \begin{bmatrix} 10 & -4 \\ -8 & -2 \end{bmatrix} = \begin{bmatrix} 22 & -3 \\ -18 & 0 \end{bmatrix}$

The final result is: $3A^T - B + 2C = \begin{bmatrix} 22 & -3 \\ -18 & 0 \end{bmatrix}$

Would you like a detailed explanation for the next question or clarification on this one?

Here are 5 related questions you might explore:

1. How do you find the inverse of a 2x2 matrix?
2. What are the properties of matrix addition and scalar multiplication?
3. How does transposing a matrix affect its properties?
4. Can every matrix be inverted? If not, why?
5. What is the geometric interpretation of matrix multiplication?

Tip: Always check if matrices are compatible in size before performing operations like addition and multiplication.