https://file.aiquickdraw.com/mathbot/file/1727335996993cvsopuh3.jpg

Let's break down the problem given in the image.

The equation is:

\[
2 \begin{pmatrix} \frac{a}{3} & 2 \\ 1 & \end{pmatrix} + \begin{pmatrix} 4 & 0 \\ -1 & b \end{pmatrix} = \begin{pmatrix} 3 & \frac{2}{4} \\ \frac{2}{1} & \frac{d}{3} \end{pmatrix}
\]

To find the value of \( a + b + c + d \), we need to solve for each variable by equating the elements on both sides of the matrices.

### 1. Solve for \( a \):
\[
2 \cdot \frac{a}{3} + 4 = 3
\]
\[
\frac{2a}{3} + 4 = 3
\]
\[
\frac{2a}{3} = -1
\]
\[
a = -\frac{3}{2}
\]

### 2. Solve for \( b \):
\[
2 \cdot 1 + b = \frac{d}{3}
\]

### 3. Solve for \( c \):
\[
2 = \frac{2}{4}
\]

### 4. Solve for \( d \):
\[
1 = \frac{d}{3}
\]
\[
d = 3
\]

Finally, calculate \( a + b + c + d \). The possible options are given as:

- 13
- 15
- 17
- 19

Let's now compute.

Jika 2((a/3) 2, 1) + (4 0, -1 b) = (3 (2/4), (2/1) (d/3)), nilai a + b + c + d = ....

Learn how to solve matrix equations by performing scalar multiplication and matrix addition to find the values of variables a, b, c, and d. This problem covers key concepts such as matrix addition and scalar multiplication. Suitable for students in Grades 10-12.

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