please see the picture.                                   1.
a）In R2 write down the matrix representations AR1 , AR2 and AR3 where i. R1 is reflection in the line y = −x, 
ii. R2 is rotation by π , 6 
iii. R3 scaling by 2.
b）Write down the matrix representation of the transformation T that corresponds to 
doing R3 first, then R1 and then R2.
c）Draw the effect of T on the square with corners A = (0,0),B = (1,0),C = (0,1),D = 
(1, 1).
2. 
B={x−x2,1+x,1−x2}isabasisforP2. Also,defineT :P2 →P2 byT(a0+a1x+a2x2)= 
−a0 −a2 +(a0 +a1)x+a1x2. 
a）Find the matrix representation of T, [T]S,B. (Recall that S is the standard basis.) 
b) Find ([T]S,B)−1 if possible. 
c) Using part (b), is T injective? Is T surjective? 
d) Find ker(T) and Im(T). 
3
AnotherbasisforP2 isC={2x,1+x2,x2}. 
* (a)  Write down the transition matrices PS,B and PS,C, where B is the basis from Q2. 

* (b)  Use part (a) to find PB,S. 
* c) Find the transition matrix PB,C. (d) Use PB,C and the fact that 。。

 

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