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The question provides three matrices:

\[
A = \begin{pmatrix} -2 & -1 \\ 5 & 3 \end{pmatrix}, 
B = \begin{pmatrix} 4 & 3 \\ -6 & 0 \end{pmatrix}, 
C = \begin{pmatrix} -3 & -6 \\ -3 & -2 \end{pmatrix}
\]

The task is to calculate the result of \(2A + BC\), where:

1. \(2A\) is the matrix \(A\) scaled by 2.
2. \(BC\) is the matrix product of matrices \(B\) and \(C\).

Let's calculate \(2A\) and \(BC\) step by step.

### Step 1: Calculate \(2A\)
\[
2A = 2 \times \begin{pmatrix} -2 & -1 \\ 5 & 3 \end{pmatrix} = \begin{pmatrix} -4 & -2 \\ 10 & 6 \end{pmatrix}
\]

### Step 2: Calculate \(BC\)
To calculate the product \(BC\), we perform matrix multiplication between \(B\) and \(C\):
\[
B = \begin{pmatrix} 4 & 3 \\ -6 & 0 \end{pmatrix}, \quad C = \begin{pmatrix} -3 & -6 \\ -3 & -2 \end{pmatrix}
\]
The matrix multiplication \(BC\) is calculated as follows:

\[
BC = \begin{pmatrix} (4 \times -3) + (3 \times -3) & (4 \times -6) + (3 \times -2) \\ (-6 \times -3) + (0 \times -3) & (-6 \times -6) + (0 \times -2) \end{pmatrix}
\]

\[
BC = \begin{pmatrix} -12 + (-9) & -24 + (-6) \\ 18 + 0 & 36 + 0 \end{pmatrix}
\]
\[
BC = \begin{pmatrix} -21 & -30 \\ 18 & 36 \end{pmatrix}
\]

### Step 3: Calculate \(2A + BC\)
Now, we add the matrices \(2A\) and \(BC\):

\[
2A + BC = \begin{pmatrix} -4 & -2 \\ 10 & 6 \end{pmatrix} + \begin{pmatrix} -21 & -30 \\ 18 & 36 \end{pmatrix}
\]
\[
2A + BC = \begin{pmatrix} -4 + (-21) & -2 + (-30) \\ 10 + 18 & 6 + 36 \end{pmatrix}
\]
\[
2A + BC = \begin{pmatrix} -25 & -32 \\ 28 & 42 \end{pmatrix}
\]

Thus, the result of \(2A + BC\) is:

\[
\begin{pmatrix} -25 & -32 \\ 28 & 42 \end{pmatrix}
\]

Would you like more details or have any questions?

Here are five related questions:
1. How do you compute the product of two matrices?
2. What is the general formula for multiplying two 2x2 matrices?
3. How do you find the scalar multiple of a matrix?
4. What are the properties of matrix addition?
5. Can matrix multiplication be commutative?

**Tip**: Always ensure the number of columns in the first matrix matches the number of rows in the second matrix when performing matrix multiplication!

Jika diketahui matriks A = [-2 -1; 5 3], B = [4 3; -6 0], dan C = [-3 -6; -3 -2], maka hasil dari: 2A + BC adalah ...

Solve a matrix problem involving scalar multiplication and matrix multiplication for matrices A, B, and C. This problem covers key matrix operations suitable for Grades 10-12, with a step-by-step breakdown of 2A + BC.

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