linear transformation: reflect thru hor. axis, then thru....

[beavis]

Find the standard matrix for the linear transformation T from R^2 to R^2 that first reflects points through the horizontal x1 axis and then reflects points through the line x2=x1

 

[pka]

You need to rewrite this "x1 axis and then reflects points through the line x2=x1"
Do you mean the x-axis? If not what is x1?
What does the line x2=x1 mean? Is that the line y=x?

 

[beavis]

yes x1 is the x axis, and x=y. Sorry, we have to use the same terminology that my instructor likes.

 

[pka]

Well then you want the mapping \(\displaystyle (p,q) \to \left( { - q,p} \right)\).
Then \(\displaystyle \left[ {\begin{array}{lr} 0 & { - 1} \\ 1 & 0 \\\end{array}} \right]\left[ {\begin{array}{r} p \\ q \\\end{array}} \right] = \left[ {\begin{array}{r} { - q} \\ p \\\end{array}} \right]\)

You will have to put that into your instructor's notation.