https://file.aiquickdraw.com/mathbot/file/17271503480929b2q8o0y.jpg

Let's start by solving question 1 from the uploaded image. 

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

Find \( 2A - B + 3C^T \).

1. **Calculate \( 2A \):**

\[
2A = 2 \times \begin{bmatrix} 3 & -4 \\ 2 & 1 \end{bmatrix} = \begin{bmatrix} 6 & -8 \\ 4 & 2 \end{bmatrix}
\]

2. **Calculate \( -B \):**

\[
-B = \begin{bmatrix} 3 & 2 \\ 1 & -5 \end{bmatrix}
\]

3. **Calculate \( 3C^T \) (Transpose of \( C \)):**

\[
C^T = \begin{bmatrix} 5 & -2 \\ 4 & -1 \end{bmatrix}
\]
\[
3C^T = 3 \times \begin{bmatrix} 5 & -2 \\ 4 & -1 \end{bmatrix} = \begin{bmatrix} 15 & -6 \\ 12 & -3 \end{bmatrix}
\]

4. **Combine all parts:**

\[
2A - B + 3C^T = \begin{bmatrix} 6 & -8 \\ 4 & 2 \end{bmatrix} + \begin{bmatrix} 3 & 2 \\ 1 & -5 \end{bmatrix} + \begin{bmatrix} 15 & -6 \\ 12 & -3 \end{bmatrix}
\]

Adding all these matrices element-wise:

\[
2A - B + 3C^T = \begin{bmatrix} 6 + 3 + 15 & -8 + 2 - 6 \\ 4 + 1 + 12 & 2 - 5 - 3 \end{bmatrix}
\]
\[
= \begin{bmatrix} 24 & -12 \\ 17 & -6 \end{bmatrix}
\]

So, the final result is:

\[
2A - B + 3C^T = \begin{bmatrix} 24 & -12 \\ 17 & -6 \end{bmatrix}
\]

Would you like further details or have any questions on this?

### Related Questions:
1. What is the inverse of matrix \( A \)?
2. Calculate the determinant of matrix \( B \).
3. Find the eigenvalues of matrix \( C \).
4. Determine if matrix \( A \) is orthogonal.
5. Find the product \( AB \).

**Tip:** Always check the dimensions of matrices before performing operations like multiplication or addition.

Diketahui A = [[3, -4], [2, 1]], B = [[-3, -2], [-1, 5]], dan C = [[5, 4], [-2, -1]]. Tentukan 2A - B + 3C^T !

Learn how to perform matrix operations, including matrix transposition, addition, and multiplication. This example problem involves calculating 2A - B + 3C^T using given matrices. Suitable for students in Grades 10-12.

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