Let P2(x) be the vector space of polynomials with real coefficients of degree at most 2 and p(x) = 1+3x +2x², q(x) = 3+ x+2x², r(x) = 2x + x² € P2(x). Then which of the following is/are always correct ? I. The elements of the set {p(x),q(x)} are linearly dependent. II. The elements of the set {p(x),q(x)} are linearly independent. III. The elements of the set {q(x),r(x)} are linearly dependent. IV. The elements of the set {q(x),r(x)} are linearly independent. (a) Only I and II (b) Only I (c) Only II and III (d) Only II and IV (e) Only I, III and IV

Let P2(x) be the vector space of polynomials with real coefficients of degree at most 2 and p(x) = 1+3x +2x², q(x) = 3+ x+2x², r(x) = 2x + x² € P2(x). Then which of the following is/are always correct ? I. The elements of the set {p(x),q(x)} are linearly dependent. II. The elements of the set {p(x),q(x)} are linearly independent. III. The elements of the set {q(x),r(x)} are linearly dependent. IV. The elements of the set {q(x),r(x)} are linearly independent. (a) Only I and II (b) Only I (c) Only II and III (d) Only II and IV (e) Only I, III and IV

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 15EQ

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