i was trying to figure out something that i didn't understand and the book doesn't have much examples of it either. My question is how do u know whether a transformation is a projection on a line, reflection on a line, or rotation through an angel? With T given. The questions i did from the book, i was able to find the line and reflection, since the same question was previously stated and i was able to do it, n got the answer from there, but didn't understand it.(adsbygoogle = window.adsbygoogle || []).push({});

Take T[x y]=1/2[x-y y-x] and by solving these i get [1 -1]/[-1 1] (this is not division, just goes at the bottom, its a 2x2 matrix, and the vectors r transposed) so by looking at this

[ 1 -1]

[-1 1]

how can u tell whether its a reflection, projection or rotation?

Similarly another result i got for another part was

[1/2 root3/2]

[root3/2 1/2 ]

i think this one is rotation but how can u tell?

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# Homework Help: Linear Transformation question

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