Consider the transformation T : P 2 </msub> &#x2192; P 2 </msub> ,

Emmy Knox

Emmy Knox

Answered question

2022-06-22

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

Answer & Explanation

Korotnokby

Korotnokby

Beginner2022-06-23Added 19 answers

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

Devin Anderson

Beginner2022-06-24Added 6 answers

oh i got it! thank you!

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