11. Describe, in words, the transforming effect of the matrix representation of the linear transformation [; :] 1 A = which transforms a vector x from R² → R².
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I reached this same conclusion " Tx=Ax1x2⇒Tx=0110x1x2⇒Tx=x2x1" but had difficulty explaining it in words because it is only a reflection with respect to the y=x line if there is a negative value in either the x or y original vector.
eg. (-3,2) => (2,-3) reflects across the x and y axis
however if both values of x,y are negative of positive the values stay in the same quadrant and the reflection occurs over a corresponding diagonal midline.
As far as I can tell, the values are transpose vectors of one another, but transpose is not a linear transformation. I know I must be confusing some theorem or missing something, but I cannot find it. Is there something I am misinterpretting?
Sometimes online classes are extra difficult when asking for clarification isn't immediate or easy, so sorry for the needed follow up.
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