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b) Let P2(R) be the polynomial space of all polynomials of degree less than or equal to 2 whose coefficients are on R ('R' stands for set of real numbers). Which of the following sets S are linearly independent of P2(R)? Justify your answer. i)S = {1+x, x +x?, 1+x2}; ii) S = {1+ x,2- x+ x2,-1+3x + x2}; iii) S = {1+ x,1+ x2,1-x+x?}3; iv) S = {1– 2x, 2x - x2,1-x2,1+ x²}; v) S = {x, 2x- x², 3x + 2x2).

b) Let P2(R) be the polynomial space of all polynomials of degree less than or equal to 2 whose coefficients are on R ('R' stands for set of real numbers). Which of the following sets S are linearly independent of P2(R)? Justify your answer. i)S = {1+x, x +x?, 1+x2}; ii) S = {1+ x,2- x+ x2,-1+3x + x2}; iii) S = {1+ x,1+ x2,1-x+x?}3; iv) S = {1– 2x, 2x - x2,1-x2,1+ x²}; v) S = {x, 2x- x², 3x + 2x2).

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.4: Zeros Of A Polynomial
Problem 29E
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b) Let P2(R) be the polynomial space of all polynomials of degree less than or equal to 2 whose coefficients are on R ('R' stands for set of real numbers). Which of the following sets S are linearly independent of P2(R)? Justify your answer. i) S = {1+x,x +x², 1+x?}; ii) S = {1+x,2 - x+ x2,-1+3x + x2}; iii) S = {1+x,1+ x2,1-x+x²}; iv) S = {1– 2x, 2x - x2,1-x2,1 + x²}; v) S = {x, 2x - x², 3x + 2x2). | (1 -2 O 3)
Transcribed Image Text:b) Let P2(R) be the polynomial space of all polynomials of degree less than or equal to 2 whose coefficients are on R ('R' stands for set of real numbers). Which of the following sets S are linearly independent of P2(R)? Justify your answer. i) S = {1+x,x +x², 1+x?}; ii) S = {1+x,2 - x+ x2,-1+3x + x2}; iii) S = {1+x,1+ x2,1-x+x²}; iv) S = {1– 2x, 2x - x2,1-x2,1 + x²}; v) S = {x, 2x - x², 3x + 2x2). | (1 -2 O 3)
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