https://file.aiquickdraw.com/mathbot/file/17270775086144kgriutl.jpg

In the image, we are given two matrices, \( A \) and \( B \), and the condition \( A = B \). We need to find the sum of \( a + b + c \).

The matrices are:

\[
A = \begin{pmatrix}
4a & 8 & 4 \\
6 & -1 & -3b \\
5 & 3c & 9
\end{pmatrix}
\quad \text{and} \quad
B = \begin{pmatrix}
12 & 8 & 4 \\
6 & -1 & -3a \\
5 & b & 9
\end{pmatrix}
\]

Since \( A = B \), we can equate corresponding elements from matrices \( A \) and \( B \).

1. From the first element of the first row: \( 4a = 12 \), solving for \( a \):
   \[
   a = \frac{12}{4} = 3
   \]

2. From the third element of the second row: \( -3b = -3a \), since we found \( a = 3 \):
   \[
   -3b = -9 \quad \Rightarrow \quad b = 3
   \]

3. From the second element of the third row: \( 3c = b \), and since \( b = 3 \):
   \[
   3c = 3 \quad \Rightarrow \quad c = 1
   \]

Now, we can calculate \( a + b + c \):
\[
a + b + c = 3 + 3 + 1 = 7
\]

Thus, the value of \( a + b + c \) is \( \boxed{7} \).

Would you like further details or have any questions? Here are 5 related questions:

1. How do we determine matrix equality element by element?
2. What are the general conditions for two matrices to be equal?
3. Can matrix operations like addition and scalar multiplication affect matrix equality?
4. How would the problem change if the dimensions of the matrices were different?
5. What other types of equations can arise from matrix element comparisons?

**Tip:** In matrix problems, equating corresponding elements is essential for solving unknowns efficiently!

Diketahui matriks A dan B. Jika A = B, maka a + b + c = ...

Learn how to solve a matrix equality problem by comparing corresponding elements to find the values of a, b, and c. In this example, matrix A is set equal to matrix B, and solving the equations gives the result a + b + c = 7. This lesson is suitable for students in Grades 10-12 studying linear algebra.

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