Linear transformatiom

Btuce

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I have a question in these exercise, it tells me to find a linear transformation such as Nu f= S and Nu (f o f)= T. I dont understand where did it came F (0,1,0)= (0,1,0) and alpha=1 and beta=-1. Please give a concrete answer,thanks.
 

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I have a question in these exercise, it tells me to find a linear transformation such as Nu f= S and Nu (f o f)= T. I dont understand where did it came F (0,1,0)= (0,1,0) and alpha=1 and beta=-1. Please give a concrete answer,thanks.
Attachment too faint - cannot read!
 
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