Consider the transformation T : P 2 → P 2 , where P 2 is the space of second-degree polynomials matrices, given by T ( f ) = f ( − 1 ) + f ′ ( − 1 ) ( t + 1 ). Find the matrix for this transformation relative to the standard basis A = { 1 , t , t 2 }. Can someone explain to me how to find the matrix of the transformation

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Consider the transformation   T  :      P    2    →      P    2  , where       P    2   is the space of second-degree polynomials matrices, given by   T  (  f  )  =  f  (  −  1  )  +  f  ′  (  −  1  )  (  t  +  1  ). Find the matrix for this transformation relative to the standard basis    A  =  {  1  ,  t  ,      t    2    }. Can someone explain to me how to find the matrix of the transformation

Korotnokby · Accepted Answer

For example: our third basis vector is       t    2  . We find that  T  (      t    2    )  =  (  −  1      )    2    +  2  (  −  1  )  ⋅  (  t  +  1  )  =  (  −  1  )  1  +  (  −  2  )  t  +  (  0  )      t    2  we therefore find that the third column of our matrix is   (  −  1  ,  −  2  ,  0  ).  Proceed in a like fashion for the remaining columns.

Devin Anderson · Accepted Answer

oh i got it! thank you!

Consider the transformation T : P 2 → P 2 , where P 2 is...

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