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TsAmE
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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