3) For each transformation, find the 2 x 2 matrix that corresponds to T by finding the images of (1,0) and (0,1). Find the determinant of T. e) Projection: given a fixed vector line spanned by 7 (a, b), T maps each point to the closest point on the F12 a2 ab a2+b2 a2 b2 = 0 Answer in book: det b2 ab a2+b2 12+b2 f) Reflection: given a fixed vector 7 = (a, b), T maps each point to its reflection with respect to r T(x - 2x, = 2x, - F 'a2-b2 2ab a2+b2 a2+b2 -1 Answer in book: det b2-а? 2ab a2+b2 a2+b2

Question

How did they get these answeres for e and f. I have listed answers with questions but dont know how they got them

3) For each transformation, find the 2 x 2 matrix that corresponds to T by finding the images
of (1,0) and (0,1). Find the determinant of T.
e) Projection: given a fixed vector
line spanned by 7
(a, b), T maps each point to the closest point on the
F12
a2
ab
a2+b2
a2 b2
= 0
Answer in book: det
b2
ab
a2+b2
12+b2
f) Reflection: given a fixed vector 7 = (a, b), T maps each point to its reflection with respect
to r
T(x - 2x,
= 2x, - F
'a2-b2
2ab
a2+b2
a2+b2
-1
Answer in book: det
b2-а?
2ab
a2+b2
a2+b2
Expand
Transcribed Image Text

3) For each transformation, find the 2 x 2 matrix that corresponds to T by finding the images of (1,0) and (0,1). Find the determinant of T. e) Projection: given a fixed vector line spanned by 7 (a, b), T maps each point to the closest point on the F12 a2 ab a2+b2 a2 b2 = 0 Answer in book: det b2 ab a2+b2 12+b2 f) Reflection: given a fixed vector 7 = (a, b), T maps each point to its reflection with respect to r T(x - 2x, = 2x, - F 'a2-b2 2ab a2+b2 a2+b2 -1 Answer in book: det b2-а? 2ab a2+b2 a2+b2

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