Transformation problem

1. Aug 7, 2008

takercena

Question: Find the images of the lines r = i - j + n(i + j + k) under transformation
M (matrix 3 x 3) =
(2 1 4)
(3 5 1)
(1 2 0)
in vector form.

2. Aug 7, 2008

HallsofIvy

Staff Emeritus
The image under the transformation is just that matrix times the vector? But what is n? My first thought was that it was the parameter but then that is just a single line. If that is correct then r= i- j+ n(i+ j+ k)= (n+1)i+ (n-1)j+ nk and its image is
$$\left[\begin{array}{ccc}2 & 1 & 4 \\ 3 & 5 & 1 \\ 1 & 2 & 0\end{array}\right]\left[\begin{array}{c} n+1 \\ n-1 \\ n\end{array}\right]$$

3. Aug 7, 2008

takercena

Thank you. There is some confusion here. I am confuse when to use inverse matrix to find transformation. Can you explain this. Example : 1. Find the images under the transformation

Last edited: Aug 7, 2008
4. Aug 7, 2008

HallsofIvy

Staff Emeritus
I have no idea what you mean by that. You use the inverse matrix in order to find an "inverse image": x such that Mx= y. Given a matrix M, the image of x is, by definition Mx.