https://file.aiquickdraw.com/mathbot/file/1726018324781ylwoln11.jpg

Let's analyze the problem presented in the image.

The equation in question is:

\[
\begin{pmatrix} 5 & 7 \\ -1 & -5 \end{pmatrix} + 2 \begin{pmatrix} -1 & 4 \\ 2 & -2 \end{pmatrix} - 3Q = \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}
\]

We are tasked with finding the sum of all elements in the matrix \( Q \).

### Step 1: Simplifying the equation

We begin by simplifying the expression on the left-hand side of the equation.

#### Multiply the second matrix by 2:
\[
2 \begin{pmatrix} -1 & 4 \\ 2 & -2 \end{pmatrix} = \begin{pmatrix} 2 \times (-1) & 2 \times 4 \\ 2 \times 2 & 2 \times (-2) \end{pmatrix} = \begin{pmatrix} -2 & 8 \\ 4 & -4 \end{pmatrix}
\]

Now the equation becomes:
\[
\begin{pmatrix} 5 & 7 \\ -1 & -5 \end{pmatrix} + \begin{pmatrix} -2 & 8 \\ 4 & -4 \end{pmatrix} - 3Q = \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}
\]

### Step 2: Add the two matrices:
\[
\begin{pmatrix} 5 & 7 \\ -1 & -5 \end{pmatrix} + \begin{pmatrix} -2 & 8 \\ 4 & -4 \end{pmatrix} = \begin{pmatrix} 5 + (-2) & 7 + 8 \\ -1 + 4 & -5 + (-4) \end{pmatrix} = \begin{pmatrix} 3 & 15 \\ 3 & -9 \end{pmatrix}
\]

Now the equation becomes:
\[
\begin{pmatrix} 3 & 15 \\ 3 & -9 \end{pmatrix} - 3Q = \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}
\]

### Step 3: Solve for \( Q \)

To isolate \( Q \), move \( 3Q \) to the right-hand side:
\[
\begin{pmatrix} 3 & 15 \\ 3 & -9 \end{pmatrix} = 3Q
\]

Now, divide both sides of the equation by 3 to solve for \( Q \):
\[
Q = \frac{1}{3} \begin{pmatrix} 3 & 15 \\ 3 & -9 \end{pmatrix} = \begin{pmatrix} 1 & 5 \\ 1 & -3 \end{pmatrix}
\]

### Step 4: Find the sum of all elements in matrix \( Q \)

The sum of the elements in matrix \( Q \) is:
\[
1 + 5 + 1 + (-3) = 4
\]

Thus, the sum of all elements in matrix \( Q \) is **4**.

### Final Answer:
The correct answer is **B. 4**.

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Do you want any further details or explanations?

Here are 5 related questions for practice:
1. If \( A + B - 2C = 0 \), how would you solve for \( C \)?
2. What is the determinant of the matrix \( \begin{pmatrix} 1 & 5 \\ 1 & -3 \end{pmatrix} \)?
3. How do you perform scalar multiplication on a matrix?
4. What is the trace of a matrix, and how is it calculated?
5. How can matrix inversion be used to solve systems of linear equations?

**Tip:** When solving matrix equations, remember that scalar multiplication distributes across each element in the matrix.

Jika \begin{pmatrix} 5 & 7 \\ -1 & -5 \end{pmatrix} + 2 \begin{pmatrix} -1 & 4 \\ 2 & -2 \end{pmatrix} - 3Q = \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}, jumlah dari semua elemen pada matriks Q adalah...

Learn how to solve a matrix equation and find the sum of all elements in matrix Q. This problem includes matrix addition, scalar multiplication, and matrix isolation. Suitable for students in Grades 9-12.

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