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Let A, B, C, and D be the following matrices:


Let V be the vector below:



Consider the vectors a, b, c, d below:


How do we order the list a,b,c,d to match the list \(\mathbf{A}^{-1} \mathbf{v}, \mathbf{B}^{-1} \mathbf{v}, \mathbf{C}^{-1} \mathbf{v}, \mathbf{D}^{-1} \mathbf{v}\)?

 Oct 2, 2020
 #1
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The right ordering is c, d, b, a.

 Oct 2, 2020
 #2
avatar+31098 
+3

A-1v  rotates v clockwise by 36degrees to a.

 

B-1v  reflects to d.

 

C-1v  goes to b, which seems to be identical to v.

 

D-1shrinks v to c.

 Oct 2, 2020

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