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The problem asks to find a 2x2 matrix \( X \) given the equation \( 3B + X = 2C \), where matrices \( B \) and \( C \) are provided as:

\[
B = \begin{bmatrix} 1 & -4 \\ 3 & 5 \end{bmatrix}, \quad C = \begin{bmatrix} 2 & -5 \\ 1 & 7 \end{bmatrix}
\]

### Steps to solve:

1. Rearrange the equation \( 3B + X = 2C \) to solve for \( X \):
   \[
   X = 2C - 3B
   \]
   
2. Compute \( 3B \):
   \[
   3B = 3 \times \begin{bmatrix} 1 & -4 \\ 3 & 5 \end{bmatrix} = \begin{bmatrix} 3 & -12 \\ 9 & 15 \end{bmatrix}
   \]
   
3. Compute \( 2C \):
   \[
   2C = 2 \times \begin{bmatrix} 2 & -5 \\ 1 & 7 \end{bmatrix} = \begin{bmatrix} 4 & -10 \\ 2 & 14 \end{bmatrix}
   \]
   
4. Subtract \( 3B \) from \( 2C \):
   \[
   X = \begin{bmatrix} 4 & -10 \\ 2 & 14 \end{bmatrix} - \begin{bmatrix} 3 & -12 \\ 9 & 15 \end{bmatrix} = \begin{bmatrix} 4 - 3 & -10 + 12 \\ 2 - 9 & 14 - 15 \end{bmatrix}
   \]
   \[
   X = \begin{bmatrix} 1 & 2 \\ -7 & -1 \end{bmatrix}
   \]

Thus, the matrix \( X \) is:

\[
X = \begin{bmatrix} 1 & 2 \\ -7 & -1 \end{bmatrix}
\]

Would you like further clarification on any steps?

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Here are 5 related questions you might consider:

1. How do you calculate the determinant of matrix \( X \)?
2. What is the inverse of matrix \( B \), if it exists?
3. How do matrix operations (like addition and scalar multiplication) affect determinants?
4. Can you find the eigenvalues of matrix \( B \)?
5. What are the conditions for two matrices to be invertible?

**Tip**: When solving matrix equations, always carefully apply operations to each element to avoid errors.

Diketahui B = [1 -4; 3 5] dan C = [2 -5; 1 7]. Tentukan matriks X berordo 2x2 jika 3B + X = 2C!

Find the 2x2 matrix X given the equation 3B + X = 2C, where B and C are known matrices. This problem involves matrix addition and scalar multiplication. Suitable for high school students in Grades 9-12.

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