Emmy Knox

2022-06-22

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

Korotnokby

Beginner2022-06-23Added 19 answers

For example: our third basis vector is ${t}^{2}$. We find that

$T({t}^{2})=(-1{)}^{2}+2(-1)\cdot (t+1)=(-1)1+(-2)t+(0){t}^{2}$

we therefore find that the third column of our matrix is $(-1,-2,0)$. Proceed in a like fashion for the remaining columns.

$T({t}^{2})=(-1{)}^{2}+2(-1)\cdot (t+1)=(-1)1+(-2)t+(0){t}^{2}$

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

Beginner2022-06-24Added 6 answers

oh i got it! thank you!