https://file.aiquickdraw.com/mathbot/file/1726893994535e9k2enjb.jpg

The system of linear equations provided in the image is:

\[
\begin{aligned}
-9x + 5y &= 4 \\
9x - 2y &= 2
\end{aligned}
\]

To represent this system in matrix form, we write it as \(A\mathbf{x} = \mathbf{b}\), where:

- \(A\) is the coefficient matrix (containing the coefficients of \(x\) and \(y\)),
- \(\mathbf{x}\) is the column vector of variables \([x \ y]^T\),
- \(\mathbf{b}\) is the column vector on the right-hand side of the equations.

### Step 1: Coefficient matrix
From the system, the coefficients of \(x\) and \(y\) in the first equation are \(-9\) and \(5\), respectively. In the second equation, the coefficients are \(9\) and \(-2\).

Thus, the coefficient matrix \(A\) is:

\[
A = \begin{bmatrix}
-9 & 5 \\
9 & -2
\end{bmatrix}
\]

### Step 2: Variable matrix
The variable matrix \(\mathbf{x}\) is:

\[
\mathbf{x} = \begin{bmatrix}
x \\
y
\end{bmatrix}
\]

### Step 3: Right-hand side matrix
The right-hand side matrix \(\mathbf{b}\) contains the constants from the right-hand side of each equation, which are \(4\) and \(2\):

\[
\mathbf{b} = \begin{bmatrix}
4 \\
2
\end{bmatrix}
\]

### Full matrix form
The system can now be written as:

\[
\begin{bmatrix}
-9 & 5 \\
9 & -2
\end{bmatrix}
\begin{bmatrix}
x \\
y
\end{bmatrix}
=
\begin{bmatrix}
4 \\
2
\end{bmatrix}
\]

This represents the matrix form of the given system of equations. 

Would you like further details or have any questions? 

Here are 5 related questions you might consider:
1. How can you solve this system of linear equations using matrices?
2. What is the determinant of the coefficient matrix?
3. Can this system of equations be solved using the inverse of the matrix?
4. How does this matrix equation relate to Gaussian elimination?
5. What other methods can you use to solve a system of linear equations?

**Tip:** When converting systems of equations into matrix form, always ensure that the variables are aligned in the same order in both equations before extracting the coefficients.

Write a matrix to represent the system of linear equations: -9x + 5y = 4 and 9x - 2y = 2.

Learn how to represent the system of linear equations -9x + 5y = 4 and 9x - 2y = 2 as a matrix equation. This problem involves key concepts in linear algebra, including matrices and systems of linear equations. Suitable for high school students.

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