Find the linear transformation T : M2×2 → P2 such that (Image below) (:)T2, T= 2x + x², TI,0 00 00 0T5a?.01

T:M2×2→P2T1000=2, T0100=2x+x2, T0010=-x, T0001=5x2

Answered: (:) T 2, T = 2x +2, T = -I, 0 0 0 0 T…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Find the linear transformation T : M_2×2 → P2 such that (Image below)

(:)
T
2, T
= 2x + x², T
I,
0 0
0 0
0 0
T
5a?.
01

Expert Solution

Given

$T : M_{2 \times 2} \to P_{2} T ([\begin{matrix} 1 & 0 \\ 0 & 0 \end{matrix}]) = 2, T ([\begin{matrix} 0 & 1 \\ 0 & 0 \end{matrix}]) = 2 x + x^{2}, T ([\begin{matrix} 0 & 0 \\ 1 & 0 \end{matrix}]) = - x, T ([\begin{matrix} 0 & 0 \\ 0 & 1 \end{matrix}]) = 5 x^{2}$