https://file.aiquickdraw.com/mathbot/file/172596277784527xe2bud.jpg

Let's analyze the problem step-by-step.

The problem involves matrix operations, and we need to find the value of \( x - 2y \) from the given matrix equation.

### Given Equation:

\[
\begin{pmatrix}
12 & x+1 \\
x & 4
\end{pmatrix}
-
\begin{pmatrix}
4 & y \\
2 & -5
\end{pmatrix}
-
\left( 
\begin{pmatrix}
1 & -2 \\
4 & 3
\end{pmatrix}
\cdot
\begin{pmatrix}
2 & 3 \\
-3 & -1
\end{pmatrix}
\right)
\]

To solve this, we need to compute the matrix multiplication first, then perform matrix subtraction, and finally solve for \( x \) and \( y \).

### Step 1: Matrix Multiplication

Let's calculate:

\[
\begin{pmatrix}
1 & -2 \\
4 & 3
\end{pmatrix}
\cdot
\begin{pmatrix}
2 & 3 \\
-3 & -1
\end{pmatrix}
\]

The resulting matrix will be:

\[
\text{Result}_{11} = 1 \cdot 2 + (-2) \cdot (-3) = 2 + 6 = 8
\]
\[
\text{Result}_{12} = 1 \cdot 3 + (-2) \cdot (-1) = 3 + 2 = 5
\]
\[
\text{Result}_{21} = 4 \cdot 2 + 3 \cdot (-3) = 8 - 9 = -1
\]
\[
\text{Result}_{22} = 4 \cdot 3 + 3 \cdot (-1) = 12 - 3 = 9
\]

So, the resulting matrix is:

\[
\begin{pmatrix}
8 & 5 \\
-1 & 9
\end{pmatrix}
\]

### Step 2: Matrix Subtraction

Now, we subtract the matrices:

1. Subtract the second matrix:

\[
\begin{pmatrix}
12 & x+1 \\
x & 4
\end{pmatrix}
-
\begin{pmatrix}
4 & y \\
2 & -5
\end{pmatrix}
=
\begin{pmatrix}
12 - 4 & (x+1) - y \\
x - 2 & 4 - (-5)
\end{pmatrix}
=
\begin{pmatrix}
8 & x+1 - y \\
x - 2 & 9
\end{pmatrix}
\]

2. Subtract the multiplication result:

\[
\begin{pmatrix}
8 & x+1 - y \\
x - 2 & 9
\end{pmatrix}
-
\begin{pmatrix}
8 & 5 \\
-1 & 9
\end{pmatrix}
=
\begin{pmatrix}
8 - 8 & (x+1 - y) - 5 \\
(x - 2) - (-1) & 9 - 9
\end{pmatrix}
=
\begin{pmatrix}
0 & x - y - 4 \\
x - 1 & 0
\end{pmatrix}
\]

### Step 3: Solving for \( x \) and \( y \)

For the matrices to be equal, all corresponding elements must be equal:

1. \( x - y - 4 = 0 \implies x - y = 4 \)
2. \( x - 1 = 0 \implies x = 1 \)

Substitute \( x = 1 \) into the first equation:

\[
1 - y = 4 \implies y = -3
\]

### Step 4: Calculating \( x - 2y \)

Now, we find the value of \( x - 2y \):

\[
x - 2y = 1 - 2(-3) = 1 + 6 = 7
\]

### Answer

The value of \( x - 2y \) is **7**, which corresponds to option **C**.

Would you like further details on any part of the solution or have any questions?

### Related Questions:

1. How do you multiply two matrices with different dimensions?
2. What are the properties of matrix subtraction?
3. How do you solve a system of equations with two variables?
4. What are the types of matrices used in linear algebra?
5. How can you determine if two matrices are equal?

### Tip: 
When multiplying matrices, always ensure that the number of columns in the first matrix is equal to the number of rows in the second matrix.

Diketahui persamaan matriks (12 x+1) - (4 y) - (1 -2) * (2 3) = (8 5) maka nilai x - 2y

Learn how to solve a matrix equation by performing matrix multiplication and subtraction. This problem focuses on key algebraic concepts involving matrices and is suitable for students in Grades 10-12.

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