Matrix Transformation - mappings of functions

[Kenny52]

I need to find the matrix transformation of \(\displaystyle y = \frac{1}{x}\) onto \(\displaystyle y = \frac{-1}{3x-1}-2\)

I think its \(\displaystyle
\begin{bmatrix}
x'\\
y'
\end{bmatrix}
=\begin{bmatrix}
3 & 0 \\
0 & -1
\end{bmatrix}
\begin{bmatrix}
x\\
y
\end{bmatrix}
+
\begin{bmatrix}
-1\\
-2
\end{bmatrix}
\)

 

[jvicens]

Great start! However, I believe there may be an error in your matrix transformation. The matrix you provided would result in the transformation y' = 3x + 1, which is not equivalent to y = -1/(3x-1) - 2.

After some calculations, I believe the correct matrix transformation should be:

\begin{bmatrix}
x'\\
y'
\end{bmatrix}
=\begin{bmatrix}
-3 & 0 \\
0 & 1
\end{bmatrix}
\begin{bmatrix}
x\\
y
\end{bmatrix}
+
\begin{bmatrix}
-2\\
-1
\end{bmatrix}

This transformation would result in y' = -1/(3x-1) - 2, which is the desired outcome. It's important to double check our calculations, especially when dealing with complex equations. Great job on finding the correct transformation!