To every linear transformation T from R^2 to R^2, there is an associated 2 times

Question

To every linear transformation T from R^2 to R^2, there is an associated 2 times 2 matrix. Match the following linear transformation with their associated matrix. 1. Clockwise rotation by pi/2 radians 2. Counter-clockwise rotation by pi/2 radians 3. Reflection about the line y = x 4. The projection onto the z-axis given by T(x, y) = (x, 0) 5. Reflection about the y-axis 6. Reflection about the x-axis A. [1 0 0 -1] B. [1 0 0 0] C. [-1 0 0 1] D.[0 -1 1 0] E. [0 1 1 0] F. [0 1 -1 0] G. None of the above

Explanation / Answer

a) clockwise rotation by pi/2 = anticlockwise rotaion by 3pi/2

[ 0 , 1 , -1 , 0] Option f

b) counterclockwise by pi/2 = [ 0 , -1 , 1 , 0 ]

Option D

c) Reflection about y = x

Option E

d) Option b

e) Reflection about y axis

Option c

f) Reflection about x axis

Option a

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