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Exercise 10.3.1

Avg difficulty 3.0

Let $T:\mathbf{P}_{2}\to\mathbb{R}$ be a linear transformation such that

T(x^{2})=1,\quad T(x^{2}+x)=5,\quad\text{and}\quad T(x^{2}+x+1)=-1.

Find $T(ax^{2}+bx+c)$ .

Selinger, Matrix Theory and Linear Algebra, Linear transformation of vector spaces, Linear transformations defined on a basis, Exercise 10.3.1

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Adapted from Matrix Theory and Linear Algebra © 2017–2026 Peter Selinger, Lyryx Learning, and Ken Kuttler. Licensed under CC BY 4.0. Source: Matrix Theory and Linear Algebra. Imported at revision d74bc3a.