Exercise 8

An endomorphism of polynomials

Theory used: Associated matrix Isomorphisms and determinant The coordinate isomorphism

Let $T : R_{2} [x] \to R_{2} [x]$ , $T (p) = p + p^{'}$ . Write the matrix of $T$ with respect to the basis $(1, x, x^{2})$ , determine whether $T$ is an isomorphism and find the polynomial $p$ such that $T (p) = x^{2}$ .

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