Assistant: 
User: User: $
\begin{pmatrix}
  a & b & c \\
  d & e & f \\
  g & h & i
\end{pmatrix}
\begin{pmatrix} 2\\ 4\\ -2 \end{pmatrix}
$
Assistant: To perform the matrix multiplication, we will multiply the 3x3 matrix by the 3x1 column matrix. 

Given:

\[
A = \begin{pmatrix}
  a & b & c \\
  d & e & f \\
  g & h & i
\end{pmatrix}
\]

and 

\[
B = \begin{pmatrix} 2\\ 4\\ -2 \end{pmatrix}
\]

The product \( A \cdot B \) is calculated as follows:

\[
A \cdot B = \begin{pmatrix}
  a & b & c \\
  d & e & f \\
  g & h & i
\end{pmatrix}
\begin{pmatrix} 2\\ 4\\ -2 \end{pmatrix}
\]

To calculate each element of the resulting matrix (which will also be a 3x1 matrix):

1. **First Row**:

\[
a \cdot 2 + b \cdot 4 + c \cdot (-2) = 2a + 4b - 2c
\]

2. **Second Row**:

\[
d \cdot 2 + e \cdot 4 + f \cdot (-2) = 2d + 4e - 2f
\]

3. **Third Row**:

\[
g \cdot 2 + h \cdot 4 + i \cdot (-2) = 2g + 4h - 2i
\]

Putting it all together, we can express the resulting matrix as:

\[
\begin{pmatrix}
2a + 4b - 2c \\
2d + 4e - 2f \\
2g + 4h - 2i
\end{pmatrix}
\]

Thus, the product of the two matrices is:

\[
\begin{pmatrix}
2a + 4b - 2c \\
2d + 4e - 2f \\
2g + 4h - 2i
\end{pmatrix}
\]
User: $
\begin{pmatrix}
  a & b & c \\
  d & e & f \\
  g & h & i
\end{pmatrix}
\begin{pmatrix} 2\\ 4\\ -2 \end{pmatrix}
$
Assistant: To perform the matrix multiplication, we will multiply the 3x3 matrix by the 3x1 column matrix.

Given:

\[
A = \begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix}
\]

and 

\[
B = \begin{pmatrix} 2 \\ 4 \\ -2 \end{pmatrix}
\]

The product \( A \cdot B \) is calculated as follows:

1. **First Row**:
   \[
   a \cdot 2 + b \cdot 4 + c \cdot (-2) = 2a + 4b - 2c
   \]

2. **Second Row**:
   \[
   d \cdot 2 + e \cdot 4 + f \cdot (-2) = 2d + 4e - 2f
   \]

3. **Third Row**:
   \[
   g \cdot 2 + h \cdot 4 + i \cdot (-2) = 2g + 4h - 2i
   \]

Putting it all together, the resulting matrix is:

\[
A \cdot B = \begin{pmatrix} 2a + 4b - 2c \\ 2d + 4e - 2f \\ 2g + 4h - 2i \end{pmatrix}
\]

So, the final result of the multiplication is:

\[
\begin{pmatrix} 2a + 4b - 2c \\ 2d + 4e - 2f \\ 2g + 4h - 2i \end{pmatrix}
\]
User: $
\begin{pmatrix}
  a & b & c \\
  d & e & f \\
  g & h & i
\end{pmatrix}
\begin{pmatrix} 2\\ 4\\ -2 \end{pmatrix}
$
Assistant: One message exceeds the 1000chars per message limit. Join our discord for more: [https://discord.com/invite/q55gsH8z5F](https://discord.com/invite/q55gsH8z5F)
User: $
\begin{pmatrix}
  a & b & c \\
  d & e & f \\
  g & h & i
\end{pmatrix}
\begin{pmatrix} 2\\ 4\\ -2 \end{pmatrix}
$
Assistant: To perform the matrix multiplication, we will multiply the 3x3 matrix by the 3x1 column matrix.

Given:

\[
A = \begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix}
\]

and 

\[
B = \begin{pmatrix} 2 \\ 4 \\ -2 \end{pmatrix}
\]

The product \( A \cdot B \) is calculated as follows:

1. **First Row**:
   \[
   a \cdot 2 + b \cdot 4 + c \cdot (-2) = 2a + 4b - 2c
   \]

2. **Second Row**:
   \[
   d \cdot 2 + e \cdot 4 + f \cdot (-2) = 2d + 4e - 2f
   \]

3. **Third Row**:
   \[
   g \cdot 2 + h \cdot 4 + i \cdot (-2) = 2g + 4h - 2i
   \]

Putting it all together, the resulting matrix is:

\[
A \cdot B = \begin{pmatrix} 2a + 4b - 2c \\ 2d + 4e - 2f \\ 2g + 4h - 2i \end{pmatrix}
\]

So, the final result of the multiplication is:

\[
\begin{pmatrix} 2a + 4b - 2c \\ 2d + 4e - 2f \\ 2g + 4h - 2i \end{pmatrix}
\]
User: \begin{pmatrix}
  a & b & c \\
  d & e & f \\
  g & h & i
\end{pmatrix}
\begin{pmatrix} 2\\ 4\\ -2 \end{pmatrix}
Assistant: One message exceeds the 1000chars per message limit. Join our discord for more: [https://discord.com/invite/q55gsH8z5F](https://discord.com/invite/q55gsH8z5F)
User: \begin{pmatrix}
  a & b & c \\
  d & e & f \\
  g & h & i
\end{pmatrix}
\begin{pmatrix} 2\\ 4\\ -2 \end{pmatrix}
Assistant: To perform the matrix multiplication of the given 3x3 matrix and the 3x1 column matrix, we can follow these steps:

Given:

\[
A = \begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix}
\]

and 

\[
B = \begin{pmatrix} 2 \\ 4 \\ -2 \end{pmatrix}
\]

The product \( A \cdot B \) is calculated as follows:

1. **First Row**:
   \[
   a \cdot 2 + b \cdot 4 + c \cdot (-2) = 2a + 4b - 2c
   \]

2. **Second Row**:
   \[
   d \cdot 2 + e \cdot 4 + f \cdot (-2) = 2d + 4e - 2f
   \]

3. **Third Row**:
   \[
   g \cdot 2 + h \cdot 4 + i \cdot (-2) = 2g + 4h - 2i
   \]

Putting it all together, the resulting matrix is:

\[
A \cdot B = \begin{pmatrix} 2a + 4b - 2c \\ 2d + 4e - 2f \\ 2g + 4h - 2i \end{pmatrix}
\]

So, the final result of the multiplication is:

\[
\begin{pmatrix} 2a + 4b - 2c \\ 2d + 4e - 2f \\ 2g + 4h - 2i \end{pmatrix}
\]
User: $\begin{pmatrix}
  a & b & c \\
  d & e & f \\
  g & h & i
\end{pmatrix}
\begin{pmatrix} 2\\ 4\\ -2 \end{pmatrix}$
Assistant:
Assistant: