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Algebra and Trigonometry (6th Edition)
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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Consider the vector space P3 of polynomials of degree at most 2. Some of the statements about the polynomials x – 1 x+ 2 x? + 3 are correct and some are incorrect. Select the correct statements. If we remove the third polynomial from the list, the remaining two polynomials x – 1 x+ 2 span a 1-dimensional subspace of P3. | These three polynomials are linearly independent because the only zero linear combination of the three is when all three coefficients are 0. ) These three polynomial are a spanning set for P3. | These three polynomials are linearly independent because there are three of them and dim(P3)=3 | These three polynomials are linearly dependent because two of them are first order polynomials. If we remove the third polynomial from the list, the remaining two polynomials x – 1 x + 2 span a 2-dimensional subspace of P3
Transcribed Image Text:Consider the vector space P3 of polynomials of degree at most 2. Some of the statements about the polynomials x – 1 x+ 2 x? + 3 are correct and some are incorrect. Select the correct statements. If we remove the third polynomial from the list, the remaining two polynomials x – 1 x+ 2 span a 1-dimensional subspace of P3. | These three polynomials are linearly independent because the only zero linear combination of the three is when all three coefficients are 0. ) These three polynomial are a spanning set for P3. | These three polynomials are linearly independent because there are three of them and dim(P3)=3 | These three polynomials are linearly dependent because two of them are first order polynomials. If we remove the third polynomial from the list, the remaining two polynomials x – 1 x + 2 span a 2-dimensional subspace of P3
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