https://file.aiquickdraw.com/mathbot/file/17264222199802pttezgp.jpg

The problem in the image is asking to solve a homogeneous system of equations represented by the matrix:

\[
A = \begin{bmatrix} 
1 & -3 & 3 \\
3 & -9 & 9 
\end{bmatrix}
\]

It requires you to express the solution in reduced row echelon form (RREF) and identify the solution using parameters \( r \), \( s \), and \( t \).

### Steps to solve:

1. **Write the augmented matrix** for the homogeneous system (where the right-hand side is 0):
   \[
   \begin{bmatrix} 
   1 & -3 & 3 & | & 0 \\
   3 & -9 & 9 & | & 0 
   \end{bmatrix}
   \]

2. **Perform row reduction** (Gaussian elimination) to bring the matrix to RREF.

   Start with row 1:
   \[
   R_1 = \begin{bmatrix} 1 & -3 & 3 & | & 0 \end{bmatrix}
   \]

   Now, eliminate the leading term in row 2 by performing the operation:
   \[
   R_2 = R_2 - 3R_1
   \]
   This results in:
   \[
   R_2 = \begin{bmatrix} 0 & 0 & 0 & | & 0 \end{bmatrix}
   \]

   So the matrix becomes:
   \[
   \begin{bmatrix} 
   1 & -3 & 3 & | & 0 \\
   0 & 0 & 0 & | & 0 
   \end{bmatrix}
   \]
   This is the RREF.

3. **Interpret the solution** from the RREF. The

Consider the homogeneous system of equations with coefficient matrix: A = [[1, -3, 3], [3, -9, 9]]. Find the solution to the corresponding homogeneous system by expressing A in RREF.

Learn how to solve a homogeneous system of equations with the matrix A = [[1, -3, 3], [3, -9, 9]] by applying Gaussian elimination and finding the Reduced Row Echelon Form (RREF). This method involves key concepts in linear algebra, including row reduction and parameterizing solutions. Suitable for advanced high school and college students.

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