F : P 2 </msub> <mtext>&#xA0;to&#xA0;</mtext> P 2 </msub> to F

Semaj Christian 2022-06-25 Answered
F : P 2  to  P 2 to F : P 2  to  P 2 with the conditions that F ( p 0 ) = f, F ( p 1 ) = g, F ( p 2 ) = h where f ( x ) = x 2 + 3, g ( x ) = x 2 x, h ( x ) = 2 + x. Find the transformation matrix for F in the basis ( p 0 , p 1 , p 2 )
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Answers (2)

pheniankang
Answered 2022-06-26 Author has 22 answers
The problem is meaningless without the knowledge of p 0 , p 1 , and p 2 . If it turns out that p 0 = 1, that p 1 = x, and that p 2 = x 2 , then, since f ( p 0 ) = 3 p 0 + p 2 , f ( p 1 ) = p 1 + p 2 , and f ( p 2 ) = 2 p 0 + p 1 , the matrix that you're after is
[ 3 0 2 0 1 1 1 1 0 ] .

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Leland Morrow
Answered 2022-06-27 Author has 11 answers
Cheers! I can only imagine it has to be this since otherwise the exercise seems to make little sense. The exercise has a second part: "What is the image of the transformation x 3 x 2 + 2 x + 1 in this transformation?" Can I solve that simply by multiplying the matrix by the vector " 3 x 2 + 2 x + 1" or, I assume, " 3 p 2 + 2 p 1 + p 0 "?

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