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The problem you've shared involves solving for the variables \(a\), \(b\), and \(c\) in a system of matrix equations. Let's break it down step by step.

### For part (a):
The equation given is:
\[
\begin{pmatrix}
-1 & 0 \\
3 & 2 \\
5 & 2
\end{pmatrix}
- 3 \cdot 
\begin{pmatrix}
0 & -1 \\
5 & 4 \\
-3 & 4
\end{pmatrix}
= 
\begin{pmatrix}
a & 3 \\
-12 & 2b \\
-7c & -10
\end{pmatrix}
\]

We first calculate the left-hand side. Multiply the second matrix by 3:
\[
3 \cdot 
\begin{pmatrix}
0 & -1 \\
5 & 4 \\
-3 & 4
\end{pmatrix}
=
\begin{pmatrix}
0 & -3 \\
15 & 12 \\
-9 & 12
\end{pmatrix}
\]

Now subtract:
\[
\begin{pmatrix}
-1 & 0 \\
3 & 2 \\
5 & 2
\end{pmatrix}
-
\begin{pmatrix}
0 & -3 \\
15 & 12 \\
-9 & 12
\end{pmatrix}
=
\begin{pmatrix}
-1 & 3 \\
3 - 15 & 2 - 12 \\
5 + 9 & 2 - 12
\end{pmatrix}
=
\begin{pmatrix}
-1 & 3 \\
-12 & -10 \\
14 & -10
\end{pmatrix}
\]

Equating the matrices:
\[
\begin{pmatrix}
a & 3 \\
-12 & 2b \\
-7c & -10
\end{pmatrix}
=
\begin{pmatrix}
-1 & 3 \\
-12 & -10 \\
14 & -10
\end{pmatrix}
\]

From this, we find:
1. \(a = -1\)
2. \(2b = -10 \implies b = -5\)
3. \(-7c = 14 \implies c = -2\)

---

### For part (b):
The equation given is:
\[
\begin{pmatrix}
-1 & 5 & 2 \\
3 & 2 & 4 \\
-2 & 1 & 0
\end{pmatrix}
+ 2 \cdot 
\begin{pmatrix}
1 & a & 5 \\
-4 & -2 & 2 \\
a + b & 3 - 2c & -1
\end{pmatrix}
=
\begin{pmatrix}
1 & 1 & 12 \\
-5 & -2 & 8 \\
-4 & 7 & 3b
\end{pmatrix}
\]

First, multiply the second matrix by 

Tentukan nilai variabel a, b, dan c pada operasi matriks berikut.

Learn how to solve for the variables a, b, and c in matrix equations involving scalar multiplication, matrix addition, and matrix equality. This example problem is solved step-by-step using key matrix operation formulas. Suitable for undergraduate or senior high school students.

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