Let R2 [x] be the vector space of polynomials of degree m is small or equal to 2. Consider the two following bases: the canonical E = {f1; x; x2}and a nest base B as follows B = {1; 1 + x; (1 + x) ^2}. Answer the following questions reasonably: (a) What are the coordinates in the base B of the vector p(x) = -x2+ 4? (b) And the coordinates in the canonical base E of the vector q (x) than in the base Bte coordinates (1; 1; 1) B? (c) Let U1= {p(x) 2 R2[x] j p(0) = 0} į U2 = {p(x) 2 R2[x] j p(0) = 1} Are U1 and U2 vector spaces of R2(x]? Reason your answer, proving it in affirmative case.

Let R2 [x] be the vector space of polynomials of degree m is small or equal to 2. Consider the two following bases: the canonical E = {f1; x; x2}and a nest base B as follows B = {1; 1 + x; (1 + x) ^2}. Answer the following questions reasonably: (a) What are the coordinates in the base B of the vector p(x) = -x2+ 4? (b) And the coordinates in the canonical base E of the vector q (x) than in the base Bte coordinates (1; 1; 1) B? (c) Let U1= {p(x) 2 R2[x] j p(0) = 0} į U2 = {p(x) 2 R2[x] j p(0) = 1} Are U1 and U2 vector spaces of R2(x]? Reason your answer, proving it in affirmative case.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 24EQ

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