please send complete handwritten solution for Q1 Note och meaning and 1.Let Pn = {ao+ a1x + a2x² +· ·+ anx" | ao, a1,degree highest n. Form the operator (function) T: P2→ P2, p → T (p) = p' + p, where p' is theusual derivative of the polynomial p. Also form the multplication operator î : P2→ P3, &(p) = xp.(For example it applies that T (x) =1+x och & (x) = x²).an E R} Be the amount of allpolynomial of(a) Explain in detail why P, forming a yector space. Also explain why Sn = (1, x, x², . .. ,x") form abase for Pn. (we call this the standard base Pn).(b) Justify why ât och T are linear transformations.(c) Determine the standard matrices [â] och [T] for ât and Tin the base Sn (for the appropriate n). Alsodetermine [â o T] and [T o â±]. It applies that t o T=To£?

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1. Let Pn = {ao+ a1x + a2x² +...+ anx" | ao, a1, · · · an E R} Be the amount of allpolynomial of degree highest n. Form the operator (function) T: P2 → P2, p + T (p) = p' + p, where p' is the usual derivative of the polynomial p. Also form the multplication operator â : P2→ P3, î (p) = xp. (For example it applies that T (x) =1+x och â (x) = x²). р. (a) Explain in detail why P, forming a vector space. Also explain why Sn = (1, x, x², - .. , x") form a base for Pn. (we call this the standard base Pn). (b) Justify why ôc och T are linear transformations. (c) Determine the standard matrices [â] och [T] for î and Tin the base Sn (for the appropriate n). Also determine [â o T]and [To î]. It applies that oT=Toî?

1. Let Pn = {ao+ a1x + a2x² +...+ anx" | ao, a1, · · · an E R} Be the amount of allpolynomial of degree highest n. Form the operator (function) T: P2 → P2, p + T (p) = p' + p, where p' is the usual derivative of the polynomial p. Also form the multplication operator â : P2→ P3, î (p) = xp. (For example it applies that T (x) =1+x och â (x) = x²). р. (a) Explain in detail why P, forming a vector space. Also explain why Sn = (1, x, x², - .. , x") form a base for Pn. (we call this the standard base Pn). (b) Justify why ôc och T are linear transformations. (c) Determine the standard matrices [â] och [T] for î and Tin the base Sn (for the appropriate n). Also determine [â o T]and [To î]. It applies that oT=Toî?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 70EQ

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