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## Homework Statement

Let T: [itex]\mathbb{R}^3 \to \mathbb{R}^3[/itex] be the linear map represented by the matrix [itex]\begin{pmatrix} 4 & -1 & 0 \\ 6& 3 & -2\\ 12& 6 & -4\end{pmatrix}[/itex]

What is the image under T of the plane [itex]2x - 5y + 2z = -5[/itex]?

## Homework Equations

None

## The Attempt at a Solution

I made [itex]z = \mu[/itex] and [itex]y = \lambda[/itex] (since z and y are both excess variables) and so got the parametric equations of my plane to be:

[itex]x = \frac{-5}{2} + \frac{5}{2}\lambda - \mu[/itex]

[itex]y = \lambda[/itex]

[itex]z = \mu[/itex]

where [itex]\mu, \lambda\varepsilon \mathbb{R}[/itex] but the correct answer was:

[itex]\begin{pmatrix}x\\y \\z\end{pmatrix} = \begin{pmatrix}1\\3 \\4\end{pmatrix} + \lambda \begin{pmatrix}5\\2 \\0\end{pmatrix} + \mu\begin{pmatrix}1\\0 \\-1\end{pmatrix}[/itex]

Im not sure what I did wrong